CareerKit

Aptitude Questions and Answers for Placements

Quantitative aptitude and logical reasoning questions in the style of TCS, Infosys, Wipro and AMCAT placement tests, with formulas, worked solutions and shortcuts.

12 free answers from our Aptitude & Reasoning Practice ebook, which has all 300 questions.

Percentages, profit and loss

Percentage basics

  • x% of N = N × x ÷ 100
  • A is what % of B = A ÷ B × 100
  • Increase by r%: multiply by (100 + r) ÷ 100. Decrease by r%: multiply by (100 − r) ÷ 100.
  • If A is r% more than B, then B is r ÷ (100 + r) × 100 % less than A.
  • Successive changes of a% and b%: net change = a + b + ab ÷ 100 (use negative numbers for decreases).
  • If price rises by r%, consumption must fall by r ÷ (100 + r) × 100 % to keep spending the same.

Fractions worth memorising

  • 50% = 1/2, 33⅓% = 1/3, 25% = 1/4, 20% = 1/5, 16⅔% = 1/6
  • 14 2/7% = 1/7, 12.5% = 1/8, 11 1/9% = 1/9, 10% = 1/10, 9 1/11% = 1/11

Profit, loss and discount

  • Profit = SP − CP. Profit % = Profit ÷ CP × 100 (always on cost price unless stated).
  • SP = CP × (100 + profit %) ÷ 100, or CP × (100 − loss %) ÷ 100.
  • Discount is on the marked price (MP): SP = MP × (100 − discount %) ÷ 100.
  • Two items sold at the same price, one at x% profit and one at x% loss: always a net loss of x² ÷ 100 %.
  • False weight: profit % = error ÷ (true weight − error) × 100.
  • GST is added on top of the price: price with 18% GST = price × 1.18.

What is 35% of 640?

(a) 214 · (b) 224 · (c) 232 · (d) 244

Answer: (b) 224

640 × 35 ÷ 100 = 224.

Shortcut: 10% of 640 is 64, so 30% is 192 and 5% is 32. 192 + 32 = 224.

18 is what percent of 72?

(a) 20% · (b) 22.5% · (c) 25% · (d) 28%

Answer: (c) 25%

18 ÷ 72 × 100 = 25%.

Shortcut: 18 is one quarter of 72, and 1/4 = 25%.

Time, speed and distance

Core formulas

  • Speed = Distance ÷ Time. Keep units consistent.
  • km/h to m/s: multiply by 5/18. m/s to km/h: multiply by 18/5. (So 18 km/h = 5 m/s, 36 km/h = 10 m/s, 72 km/h = 20 m/s.)
  • Average speed = total distance ÷ total time, not the average of the speeds.
  • Same distance at speeds x and y: average speed = 2xy ÷ (x + y).
  • For a fixed distance, time is inversely proportional to speed: speed ratio a : b means time ratio b : a.

Relative speed and trains

  • Moving in opposite directions: add the speeds. Same direction: subtract them.
  • A train passing a pole or a standing person covers its own length.
  • A train passing a platform, bridge or tunnel covers its length + the platform's length.
  • Two trains passing each other cover the sum of their lengths, at their relative speed.

Boats and streams

  • Downstream speed = boat + stream. Upstream speed = boat − stream.
  • Boat speed in still water = (downstream + upstream) ÷ 2. Stream speed = (downstream − upstream) ÷ 2.

Races and circular tracks

  • "A beats B by x metres" means when A finishes, B is x metres behind.
  • On a circular track of length L, two runners meet for the first time after L ÷ (relative speed).

Convert 72 km/h into metres per second.

(a) 18 m/s · (b) 20 m/s · (c) 22 m/s · (d) 25 m/s

Answer: (b) 20 m/s

72 × 5 ÷ 18 = 20 m/s.

Convert 15 m/s into km/h.

(a) 45 km/h · (b) 50 km/h · (c) 54 km/h · (d) 60 km/h

Answer: (c) 54 km/h

15 × 18 ÷ 5 = 54 km/h.

Time and work

Core ideas

  • If A finishes a job in a days, A does 1/a of it per day.
  • Working together, rates add: 1/a + 1/b. Time together = 1 ÷ (sum of rates).
  • Two people: time together = ab ÷ (a + b).
  • LCM method: take the total work as the LCM of the days. With 12 and 18 days, work = 36 units; A does 3 units a day, B does 2.
  • If A is k times as efficient as B, A takes 1/k of B's time.

Men, days and hours

  • M1 × D1 × H1 ÷ W1 = M2 × D2 × H2 ÷ W2 (men, days, hours per day, work done).

Pipes and cisterns

  • An inlet adds +1/a per hour; an outlet or leak subtracts −1/b per hour.
  • If the net rate is negative, the tank empties.

Wages

  • Wages are shared in the ratio of work done, which for the same number of days is the ratio of the daily rates.

A can finish a job in 12 days and B in 18 days. How long will they take together?

(a) 6 days · (b) 7.2 days · (c) 7.5 days · (d) 8 days

Answer: (b) 7.2 days

LCM method: work = 36 units. A does 3 a day, B does 2, together 5. 36 ÷ 5 = 7.2 days.

Shortcut: ab ÷ (a + b) = 216 ÷ 30 = 7.2.

A and B together finish a job in 10 days. A alone takes 15 days. How long would B take alone?

(a) 25 days · (b) 35 days · (c) 30 days · (d) 40 days

Answer: (c) 30 days

Work = 30 units. Together 3 a day, A does 2, so B does 1. B takes 30 days.

Number series and coding-decoding

Number series checklist

  1. Differences between terms: constant (+4), increasing (+3, +6, +9) or a second-level pattern.
  2. Ratios: ×2, ×3, or an increasing multiplier (×2, ×3, ×4).
  3. Squares and cubes, often ± a small number (n² − 1, n³ + 1).
  4. Multiply and add: ×2 + 1, ×3 − 2.
  5. Two alternating series mixed together (odd and even positions).
  6. Special sequences: primes (2, 3, 5, 7, 11, 13...), Fibonacci (each term = sum of the previous two).

Letter positions

  • A1 B2 C3 D4 E5 F6 G7 H8 I9 J10 K11 L12 M13 N14 O15 P16 Q17 R18 S19 T20 U21 V22 W23 X24 Y25 Z26
  • Memory trick: EJOTY = 5, 10, 15, 20, 25.
  • Opposite letters add up to 27: A↔Z, B↔Y, C↔X, M↔N.

Coding-decoding approach

  • Compare each letter of the word with its code: is it a fixed shift (+1, −2), an increasing shift (+1, +2, +3), the opposite letter, or a reversal?
  • For sentence codes, compare two sentences that share a word: the common code word means the common word.

Find the next number: 3, 7, 11, 15, ?

(a) 17 · (b) 19 · (c) 21 · (d) 23

Answer: (b) 19

Each term adds 4.

Find the next number: 2, 6, 12, 20, 30, ?

(a) 40 · (b) 44 · (c) 42 · (d) 48

Answer: (c) 42

The terms are 1×2, 2×3, 3×4, 4×5, 5×6, so the next is 6×7 = 42. (Differences: 4, 6, 8, 10, 12.)

Blood relations and seating arrangement

Blood relations

  • Draw a family tree: generations in rows, a line down for parent and child, = for a married couple. Mark males (+) and females (−).
  • Decode phrases from the end, one step at a time: "my father's only son" is me (if I'm male) or my brother.
  • "Only daughter of my mother" when the speaker is a woman means the speaker herself.
  • If a person's gender isn't given, the answer may be "brother or sister" (or "can't be determined").
  • Indian terms help: father's sister = bua, her husband = phupha; mother's brother = mama; father's younger brother = chacha.

Seating arrangement

  • Row facing north: your right is the right end of the row. Facing south, left and right flip.
  • Circle facing the centre: your left is clockwise, your right is anticlockwise.
  • Circle facing outward: your left is anticlockwise, your right is clockwise.
  • Opposite seats exist only with an even number of people; with n people, opposite = n/2 seats away.
  • Start with the most definite clue (an end seat, the middle, an "opposite"), then place the rest.

Position in a row

  • Position from the right = total − position from the left + 1.
  • Total = position from the left + position from the right − 1.

Pointing to a man, Neha says, "He is the son of my grandfather's only son." How is the man related to Neha?

(a) Brother · (b) Cousin · (c) Uncle · (d) Father

Answer: (a) Brother

Neha's grandfather's only son is her father. The son of her father is her brother.

Pointing to a girl in a photograph, Arjun says, "Her mother is the only daughter of my mother." How is Arjun related to the girl?

(a) Father · (b) Brother · (c) Maternal uncle · (d) Cousin

Answer: (c) Maternal uncle

The only daughter of Arjun's mother is Arjun's sister. The girl's mother is Arjun's sister, so Arjun is her maternal uncle (mama).

Full practice tests

How to take these tests

  • Test 1 is questions 241 to 270; Test 2 is questions 271 to 300.
  • Set a 40-minute timer. Skip anything that takes more than 2 minutes and come back to it.
  • Most placement tests have no negative marking, but check the rules for yours. If there is none, never leave a question blank.
  • Score yourself with the answers at the end, then revise the topics where you lost marks.

Extra formulas used in the tests

  • Average = sum ÷ count. If one value changes by d in a group of n, the average changes by d ÷ n.
  • Simple interest = P × R × T ÷ 100. Compound amount = P × (1 + R/100)ᵀ.
  • Difference between CI and SI for 2 years = P × (R/100)².
  • Ratio: to combine A : B and B : C, make B the same in both.
  • Alligation: mixing prices a and b to get m, the ratio is (b − m) : (m − a).
  • Partnership: profit is shared in the ratio of capital × time.
  • Probability = favourable outcomes ÷ total outcomes. Combinations ⁿCᵣ = n! ÷ (r! (n − r)!).
  • Clock angle at h hours m minutes = |30h − 5.5m|; if over 180°, subtract it from 360°.
  • Calendar: an ordinary year shifts the day by 1, a leap year by 2. Count odd days with (days mod 7).
  • Unit digits of powers repeat in cycles of 4 (for 7: 7, 9, 3, 1).

The average of 5 numbers is 42. When one number is removed, the average of the rest is 40. What number was removed?

(a) 46 · (b) 48 · (c) 50 · (d) 52

Answer: (c) 50

Total = 5 × 42 = 210. The other four total 4 × 40 = 160. Removed = 50.

What is the simple interest on ₹12,000 at 8% a year for 3 years?

(a) ₹2,400 · (b) ₹2,880 · (c) ₹3,000 · (d) ₹3,240

Answer: (b) ₹2,880

12,000 × 8 × 3 ÷ 100 = ₹2,880.

All 300 questions in the ebook

Linked questions are answered free on this page; the rest are in the ebook.

Percentages, profit and loss

  1. What is 35% of 640?
  2. 18 is what percent of 72?
  3. A number increased by 20% becomes 540. What is the number?
  4. The price of petrol rises by 25%. By what percentage must a family reduce consumption to keep its spending the same?
  5. A salary is increased by 10% and then decreased by 10%. What is the net change?
  6. Two successive increases of 20% and 30% are equal to a single increase of:
  7. In an election between two candidates, the winner got 58% of the votes and won by 2,880 votes. How many votes were cast?
  8. A town's population is 1,25,000 and grows by 4% every year. What will it be after 2 years?
  9. Ravi spends 75% of his income. His income rises by 20% and his spending by 10%. By what percentage do his savings increase?
  10. A's salary is 25% more than B's. By what percentage is B's salary less than A's?
  11. A student needs 40% to pass. She scores 178 marks and fails by 22 marks. What are the maximum marks?
  12. 60% of a number is 48 more than 40% of it. What is the number?
  13. When sugar becomes 20% cheaper, a family can buy 6 kg more for ₹1,200. What was the original price per kg?
  14. A rectangle's length is increased by 20% and its breadth decreased by 20%. What happens to its area?
  15. 12.5% is equal to which fraction?
  16. 30% of the mangoes in a shop are rotten and 2,800 are good. How many mangoes were there in total?
  17. A 40-litre mixture of milk and water has 10% water. How much water must be added to make the water 20% of the mixture?
  18. In an exam, 65% passed English, 55% passed Maths and 25% failed both. What percentage passed both?
  19. A batsman scores 110 runs, including 3 fours and 8 sixes. What percentage of his runs did he make by running between the wickets?
  20. Meena earns ₹48,000 a month. She pays 15% as rent and spends 20% of the remainder on food. How much is left?
  21. An offer letter says CTC ₹6 LPA, with basic pay at 40% of CTC. Employee PF is 12% of basic. What is the employee's yearly PF contribution?
  22. After a 12% appraisal hike, what is the new CTC of someone earning ₹5,40,000?
  23. If x% of 500 equals 25% of 340, what is x?
  24. Two numbers are 20% and 50% more than a third number. The first is what percentage of the second?
  25. An article bought for ₹800 is sold for ₹920. What is the profit percentage?
  26. A fan is sold for ₹1,140 at a loss of 5%. What was its cost price?
  27. At what price should an article costing ₹650 be sold to make a 20% profit?
  28. The cost price of 15 pens equals the selling price of 12 pens. What is the profit percentage?
  29. A jacket with a marked price of ₹2,500 is sold at a 12% discount. What is the selling price?
  30. Successive discounts of 20% and 10% are equal to a single discount of:
  31. A shopkeeper marks goods 40% above cost and then gives a 25% discount. What is the profit percentage?
  32. Two phones are sold for ₹9,900 each, one at a 10% profit and the other at a 10% loss. What is the overall result?
  33. A dishonest shopkeeper uses a 900 g weight instead of 1 kg and sells at cost price. What is his profit percentage?
  34. A vendor buys 12 bananas for ₹30 and sells 10 bananas for ₹30. What is the profit percentage?
  35. Selling an article for ₹1,620 gives a 10% loss. At what price should it be sold for a 10% profit?
  36. The profit made by selling a book for ₹1,250 equals the loss made by selling it for ₹950. What is the cost price?
  37. By selling 30 metres of cloth, a trader gains the cost price of 6 metres. What is his profit percentage?
  38. An article is sold at an 8% profit. Had it been sold for ₹72 more, the profit would have been 14%. What is the cost price?
  39. An item costing ₹2,000 is marked 30% above cost and sold at a 10% discount. What is the profit?
  40. A shop offers "Buy 3, get 1 free". What is the effective discount?
  41. A shopkeeper gives a 20% discount and still makes a 20% profit. If the cost price is ₹500, what is the marked price?
  42. A laptop costs ₹45,000 before 18% GST. What is the final price?
  43. A bill including 18% GST comes to ₹1,180. What was the price before GST?
  44. Two items together cost ₹6,000. One is sold at a 20% profit and the other at a 10% loss, with no overall profit or loss. What was the cost of the first item?
  45. On a ₹5,000 item, how much more does a customer pay with successive discounts of 10% and 20% than with a single 30% discount?
  46. A trader's profit is 25% of the selling price. What is the profit as a percentage of the cost price?
  47. Karan buys a second-hand bike for ₹42,000, spends ₹3,000 on repairs and sells it for ₹49,500. What is his profit percentage?
  48. If the selling price of an article is doubled, the profit triples. What is the profit percentage?

Time, speed and distance

  1. Convert 72 km/h into metres per second.
  2. Convert 15 m/s into km/h.
  3. A bus covers 360 km in 4 hours 30 minutes. What is its average speed?
  4. Priya drives from Pune to Mumbai at 60 km/h and returns at 40 km/h. What is her average speed for the round trip?
  5. Walking at 4/5 of his usual speed, a man reaches office 15 minutes late. What is his usual time?
  6. A 240 m long train running at 54 km/h passes a signal pole. How long does it take?
  7. A 300 m long train at 72 km/h crosses a 500 m long platform. How long does it take?
  8. Trains of 150 m and 200 m run on parallel tracks in opposite directions at 60 km/h and 45 km/h. How long do they take to cross each other?
  9. The same two trains (150 m and 200 m, at 60 km/h and 45 km/h) now run in the same direction. How long does the faster one take to pass the slower?
  10. A train passes a man standing on a platform in 10 seconds and passes the 150 m platform itself in 22 seconds. How long is the train?
  11. A 180 m train passes a man running at 6 km/h in the same direction in 12 seconds. What is the train's speed?
  12. A boat's speed in still water is 15 km/h and the stream flows at 3 km/h. How long does it take to go 54 km downstream?
  13. A boat goes downstream at 20 km/h and upstream at 12 km/h. Find the speed of the boat in still water and of the stream.
  14. A man rows 30 km downstream and 18 km upstream, taking 3 hours each way. What is the speed of the stream?
  15. A car takes 6 hours to cover a distance at 50 km/h. At what speed must it travel to cover the same distance in 5 hours?
  16. Two cities are 450 km apart. Buses leave both cities at the same time towards each other at 70 km/h and 80 km/h. When do they meet?
  17. A thief is spotted by a policeman 200 m away. The thief runs at 10 km/h and the policeman chases at 12 km/h. How far will the thief run before being caught?
  18. A cyclist covers half a distance at 30 km/h and the other half at 60 km/h. What is the average speed?
  19. Walking at 5 km/h, a student reaches college 6 minutes late. At 6 km/h, she is 4 minutes early. How far is the college?
  20. The speeds of A and B are in the ratio 3 : 4. A takes 30 minutes more than B to cover the same distance. How long does A take?
  21. A train leaves Delhi at 6 am at 60 km/h. Another leaves at 8 am on the same route at 80 km/h. At what time does the second catch the first?
  22. On a 400 km trip, Rohan rides the first 160 km at 40 km/h and the rest at 60 km/h. What is his average speed?
  23. On a 600 m circular track, A runs at 4 m/s and B at 6 m/s, starting together in the same direction. When do they first meet?
  24. On the same 600 m track, A (4 m/s) and B (6 m/s) start together but run in opposite directions. When do they first meet?
  25. A man walks to a place and rides back in 5 hours 30 minutes. Walking both ways takes 8 hours. How long would riding both ways take?
  26. The speeds of two trains are in the ratio 7 : 8. The second covers 400 km in 4 hours. What is the speed of the first?
  27. A 125 m train passes a man walking at 5 km/h in the same direction in 10 seconds. What is the train's speed?
  28. A 360 m train at 90 km/h crosses a bridge in 30 seconds. How long is the bridge?
  29. Mumbai and Pune are about 192 km apart by this route. Two trains start from them towards each other at 7 am at 60 km/h and 36 km/h. When do they meet?
  30. A boat travels 40 km downstream in 4 hours and 24 km upstream in 4 hours. What is its speed in still water?
  31. The stream flows at 4 km/h. A boat takes three times as long to go upstream as to go the same distance downstream. What is the boat's speed in still water?
  32. A man rows to a place 48 km away and back in 14 hours. He rows 4 km downstream in the time he rows 3 km upstream. What is the speed of the stream?
  33. A runs 1 km in 3 minutes and B runs it in 3 minutes 20 seconds. By how many metres does A beat B?
  34. In a 100 m race, A beats B by 10 m and B beats C by 10 m. By how many metres does A beat C?
  35. How far does a scooter travel in 20 minutes at 36 km/h?
  36. An auto travels the first 30 km at 30 km/h and the next 50 km at 50 km/h. What is its average speed?
  37. A 220 m train at 72 km/h crosses a train coming from the opposite direction at 54 km/h in 12 seconds. How long is the second train?
  38. A person travels three equal distances at 10 km/h, 20 km/h and 30 km/h. What is the average speed?
  39. Driving at 40 km/h, Arjun reaches office 10 minutes late. At 50 km/h, he is 5 minutes early. How far is the office?
  40. A 200 m train takes 30 seconds to pass completely through a 400 m tunnel. What is its speed?
  41. Two trains of equal length run on parallel tracks in the same direction at 46 km/h and 36 km/h. The faster train passes the slower in 36 seconds. How long is each train?
  42. If a car's speed is reduced by 20%, by what percentage does the time for a journey increase?
  43. A person covers one-third of a distance at 20 km/h, one-third at 30 km/h and the rest at 60 km/h. What is the average speed?
  44. A cyclist covers 12 km in 40 minutes. What is the speed in m/s?
  45. A boat covers 12 km downstream in 1 hour and the same distance upstream in 2 hours. What is the speed of the stream?
  46. A train passes a pole in 15 seconds and a 100 m bridge in 20 seconds. How long is the train?
  47. A car starts at 30 km/h and increases its speed by 5 km/h every hour. How far does it travel in 5 hours?
  48. An express train covers 1,386 km in 15 hours 45 minutes. What is its average speed?

Time and work

  1. A can finish a job in 12 days and B in 18 days. How long will they take together?
  2. A and B together finish a job in 10 days. A alone takes 15 days. How long would B take alone?
  3. A, B and C can finish a job in 10, 15 and 30 days respectively. How long will all three take together?
  4. A is twice as efficient as B. Together they finish a job in 14 days. How long would A take alone?
  5. 12 workers can complete a project in 20 days. How long will 15 workers take?
  6. 8 people working 6 hours a day finish a job in 15 days. How many days will 12 people take, working 5 hours a day?
  7. A can do a job in 20 days. A works for 5 days, then B finishes the rest in 12 days. How long would B take alone?
  8. A and B can finish a job in 12 days, B and C in 15 days, and C and A in 20 days. How long will A, B and C take together?
  9. In the previous question (A+B: 12 days, B+C: 15 days, C+A: 20 days), how long would A take alone?
  10. Pipe A fills a tank in 6 hours and pipe B in 8 hours. How long do both take together?
  11. An inlet fills a tank in 10 hours and an outlet empties it in 15 hours. If both are open, how long does the tank take to fill?
  12. A pipe fills a tank in 4 hours, but because of a leak it takes 5 hours. How long would the leak take to empty a full tank?
  13. A can do a job in 6 days and B in 8 days. Working together, they are paid ₹2,800. What is A's share?
  14. A and B can finish a job in 6 days. With C's help they finish it in 4 days and are paid ₹3,600 in total. What is C's share?
  15. 3 men or 4 women can reap a field in 43 days. How long will 7 men and 5 women take?
  16. A completes two-thirds of a job in 10 days. How long will A take for the whole job?
  17. A can finish a job in 18 days and B in 15 days. B works for 10 days and leaves. How long will A take to finish the rest?
  18. A and B can finish a job in 20 days. They work together for 4 days, then A leaves and B finishes the rest in 32 days. How long would B take alone?
  19. A is 30% more efficient than B. B alone takes 23 days. How long will they take together?
  20. Pipes A and B fill a tank in 12 and 15 minutes. Pipe C empties it in 6 minutes. If all three are opened on a full tank, how long until it's empty?
  21. 4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. How long will 10 women take?
  22. A does one-quarter of a job in 5 days and B does two-thirds of it in 20 days. How long will they take together?
  23. A can do a job in 10 days and B in 15 days. They work on alternate days, starting with A. How many days will the job take?
  24. Ravi can paint a house in 9 days and Sameer in 12 days. Ravi starts alone, and Sameer joins after 2 days. How many days does the whole job take?
  25. 20 workers build a 60 m wall in 6 days. How many days will 25 workers take to build a 100 m wall?
  26. A works twice as fast as B, and B twice as fast as C. Together they finish a job in 7 days. How long would C take alone?
  27. Two taps fill a cistern in 20 and 30 minutes. Both are opened, and after 5 minutes the first is closed. How much longer does the second take to fill it?
  28. A can do a job in 15 days and B in 10 days. They start together, but A leaves 5 days before the job is finished. How long does the job take in total?
  29. 6 men or 10 women can complete a job in 15 days. How long will 3 men and 5 women take?
  30. A can build a wall in 8 hours and B in 10 hours. With C's help, they finish it in 4 hours. How long would C take alone?
  31. 5 developers can finish a module in 24 days. After 8 days, 3 more developers join. In how many days in total is the module finished?
  32. Two pipes fill a tank in 36 and 45 minutes, and a third empties it in 30 minutes. If all three are opened together on an empty tank, how long does it take to fill?
  33. A is three times as efficient as B and takes 40 days less to finish a job. How long will they take together?
  34. 12 workers can finish a job in 18 days. After 6 days, 4 of them leave. How many more days will the rest take to finish?
  35. A, B and C can finish a job in 6, 8 and 12 days respectively. They work together and are paid ₹4,500. What is B's share?
  36. A and B together finish a job in 4 days. A alone takes 12 days. How long would B take alone?
  37. A does half a job in 5 days and B does one-third of it in 4 days. How long will they take together for the whole job?
  38. 15 workers can finish a job in 40 days. How many workers are needed to finish it in 25 days?
  39. One tap fills a tank in 3 hours, another in 6 hours, and a drain empties it in 4 hours. With all three open, how long does it take to fill?
  40. A, B and C finish a job together in 6 days. A alone takes 12 days and B alone 24 days. How long would C take alone?
  41. A takes three times as long as B to do a job. Together they finish it in 9 days. How long would A take alone?
  42. Ramesh can finish a typing job in 10 hours. With Suresh, it takes 6 hours. How long would Suresh take alone?
  43. Pipe A fills a tank in 10 minutes and pipe B in 15 minutes. Both are opened, but B is turned off after 3 minutes. How long does the tank take to fill in total?
  44. The efficiencies of A and B are in the ratio 5 : 3. B alone takes 40 days. How long will they take together?
  45. A can do a job in 25 days and B in 20 days. A works alone for some days, then B finishes the rest in 12 days. For how many days did A work?
  46. 40 workers can build a road in 60 days. After 15 days, 10 more workers join. How many more days are needed?
  47. An outlet empties a full tank in 6 hours. When an inlet adding 4 litres a minute is also open, it takes 8 hours to empty. What is the tank's capacity?
  48. A and B finish a job in 30 days, B and C in 24 days, and C and A in 20 days. All three work for 10 days, then B and C leave. How many more days does A need?

Number series and coding-decoding

  1. Find the next number: 3, 7, 11, 15, ?
  2. Find the next number: 2, 6, 12, 20, 30, ?
  3. Find the next number: 1, 4, 9, 16, 25, ?
  4. Find the next number: 5, 10, 20, 40, ?
  5. Find the next number: 2, 3, 5, 7, 11, 13, ?
  6. Find the next number: 1, 1, 2, 3, 5, 8, 13, ?
  7. Find the next number: 4, 9, 19, 39, 79, ?
  8. Find the next number: 1, 8, 27, 64, ?
  9. Find the next number: 7, 10, 16, 25, 37, ?
  10. Find the next number: 6, 11, 21, 36, 56, ?
  11. Find the next number: 120, 99, 80, 63, 48, ?
  12. Find the next number: 2, 5, 11, 23, 47, ?
  13. Find the next number: 3, 12, 48, 192, ?
  14. Find the wrong number in the series: 2, 9, 28, 65, 126, 216, 344
  15. Find the next number: 1, 2, 6, 24, 120, ?
  16. Find the next number: 1, 10, 3, 9, 5, 8, 7, 7, ?
  17. Find the next number: 0, 6, 24, 60, 120, ?
  18. Find the next number: 11, 13, 17, 19, 23, 29, ?
  19. Find the next number: 3, 6, 18, 72, 360, ?
  20. Find the next number: 4, 6, 9, 13.5, ?
  21. Find the next letter: A, C, F, J, O, ?
  22. Find the next pair: AZ, BY, CX, ?
  23. Find the next letter: B, D, G, K, P, ?
  24. Find the next letter: Z, X, U, Q, L, ?
  25. If CAT is coded as DBU, how is DOG coded?
  26. If MOUSE is coded as NPVTF, how is CHAIR coded?
  27. If TRAIN is written as NIART, how is PLANE written?
  28. If GOOD is coded as TLLW, how is BAD coded?
  29. If each letter is replaced by its position in the alphabet (A = 1), what is the sum for JOB?
  30. If DELHI is coded as 73541 and CALCUTTA as 82589662, how is CALICUT coded?
  31. If SHIP is coded as UJKR, which word is coded as EQFG?
  32. If "sky" is called "sea", "sea" is called "water", "water" is called "air" and "air" is called "cloud", where do fish live?
  33. In a code language, "123" means "hot filtered coffee", "356" means "very hot day" and "589" means "day and night". Which digit means "very"?
  34. If A = 1, B = 2 and so on, FAT = 27. What is FAITH?
  35. If APPLE = 50 using letter positions, what is GRAPE?
  36. If BREAD is coded as 52814 and CRAB as 9215, how is BARE coded?
  37. If MIRROR is coded as NJSSPS, how is WINDOW coded?
  38. If TEA is coded as UGD, how is CUP coded?
  39. If 2 × 3 = 13, 3 × 4 = 25 and 4 × 5 = 41, what is 5 × 6?
  40. If 6 + 4 = 210 and 8 + 3 = 511, what is 9 + 5?
  41. If MONKEY is coded as XDJMNL, how is TIGER coded?
  42. If ROSE is coded as 6821, CHAIR as 73456 and PREACH as 961473, how is SEARCH coded?
  43. If FRIEND is coded as HUMJTK, how is CANDLE coded?
  44. If BOOK = 43 using letter positions, what is PEN?
  45. If A = 26, B = 25, …, Z = 1, what is the value of DOG?
  46. If ZEBRA is coded as 2652181, how is COBRA coded?
  47. If MATHS is coded as NBUIT and ENGLISH as FOHMJTI, how is SCIENCE coded?
  48. In a code language, "pic vic nic" means "winter is cold", "to nic re" means "summer is hot" and "re pic boo" means "winter and summer". What is the code for "summer"?

Blood relations and seating arrangement

  1. Pointing to a man, Neha says, "He is the son of my grandfather's only son." How is the man related to Neha?
  2. Pointing to a girl in a photograph, Arjun says, "Her mother is the only daughter of my mother." How is Arjun related to the girl?
  3. A is B's sister. C is B's mother. D is C's father. E is D's mother. How is A related to D?
  4. Introducing a woman, Rohit says, "She is the wife of the only son of my father's father." How is the woman related to Rohit?
  5. P is the brother of Q, Q is the sister of R, and R is the father of S. How is P related to S?
  6. A + B means A is the mother of B; A − B means A is the brother of B; A × B means A is the father of B; A ÷ B means A is the sister of B. What does P × Q − R mean?
  7. Using the same codes (+ mother, − brother, × father, ÷ sister), which expression shows that M is the maternal grandmother of T?
  8. Rahul's mother is the only daughter of Sunita's father. How is Sunita related to Rahul?
  9. X is the husband of Y. Y is the daughter of Z. W is the son of Z. How is X related to W?
  10. Pointing to a boy, Seema says, "His father is my father's only son." How is Seema related to the boy?
  11. A is the father of B. C is the daughter of B. D is the brother of B. E is the son of A. How is C related to E?
  12. Ankit is the son of Ramesh. Priya is Ramesh's sister, and Kunal is Priya's son. How is Ankit related to Kunal?
  13. Mohan is the brother of Sohan. Sohan's father is Ramlal, and Ramlal's wife is Kamla. How is Kamla related to Mohan?
  14. X is the son of Y's brother. How is Y related to X?
  15. A woman introduces a man as the son of her mother's brother. How is the man related to the woman?
  16. Pointing to a man in a photograph, Asha says, "His mother's only daughter is my mother." How is Asha related to the man?
  17. P @ Q means P is the son of Q; P # Q means P is the daughter of Q; P $ Q means P is the wife of Q; P & Q means P is the husband of Q. If A @ B $ C, how is A related to C?
  18. Using the same codes (@ son, # daughter, $ wife, & husband), if M # N & O, how is O related to M?
  19. Vikas's father's sister's husband is Ramesh. How is Ramesh related to Vikas?
  20. Sunil's mother's mother's only son has a daughter named Riya. How is Riya related to Sunil?
  21. A is the father of B. B is the mother of C. D is the son of C. How is A related to D?
  22. Pointing to a woman, a man says, "The son of her only brother is the brother of my wife." How is the woman related to the man?
  23. Shreya is the daughter of Tarun's only sister. How is Tarun related to Shreya?
  24. A's mother is the sister of B's father, and B is a girl. How is A related to B?
  25. Five friends A, B, C, D and E sit in a row facing north. C is in the middle. A is to the immediate left of C. B is at the right end. D is not at either end. Who is at the left end?
  26. Six people P, Q, R, S, T and U sit in a row facing north. R is third from the left. P is to the immediate right of R. T is at the right end. U sits between Q and R, next to both. Who sits between P and T?
  27. Seven people J, K, L, M, N, O and P sit in a row facing north. M is in the exact middle. K is third to the right of M. J is at the left end. N is to the immediate left of M. O is second to the left of K. P is not next to J. Who is to the immediate right of J?
  28. Six friends A, B, C, D, E and F sit around a round table facing the centre. A is opposite D. B is to the immediate left of A. C is opposite B. E is to the immediate right of D. Who is to the immediate right of A?
  29. In a row of 40 students, Ravi is 12th from the left. What is his position from the right?
  30. Ananya is 14th from the left and 9th from the right in a row. How many people are in the row?
  31. In a queue, Kabir is 7th from the front and Meera is 12th from the back, with 4 people between them. If Meera is behind Kabir, how many people are in the queue?
  32. Priya ranks 16th from the top in a class of 45. What is her rank from the bottom?
  33. P is taller than Q. R is shorter than Q. S is taller than P. T is shorter than R. Who is the third tallest?
  34. Ali scored more than Bhavna but less than Chetan. Divya scored less than Bhavna. Esha scored more than Chetan. Who scored the least?
  35. Eight people A to H sit around a round table facing the centre. A is opposite E. B is to the immediate left of A. C is second to the right of E. D is opposite B. F sits between C and E. G is not next to A. Who is to the immediate right of A?
  36. Six people sit in two rows of three, facing each other. P, Q and R face south; X, Y and Z face north. Q is in the middle of the first row and X faces Q. P is at the east end, and Y faces P. Who faces R?
  37. Six people A to F sit in a row facing north. B and E sit at the two ends. D sits next to E. A sits third to the left of D. C is not next to D. Who sits between A and F?
  38. Five people P, Q, R, S and T sit around a round table facing the centre. Q is to the immediate left of P. R is second to the right of P. S is not next to P. Who sits next to both Q and R?
  39. Raju is 15th from the left and Wasim is 23rd from the right in a row of boys. When they swap places, Raju becomes 25th from the left. How many boys are in the row?
  40. Five houses in a row are painted red, blue, green, yellow and white. The red house is at the left end. The blue house is in the middle. The green house is immediately to the left of the white house. Which house is second from the left?
  41. Five people A to E live on floors 1 to 5 of a building (floor 1 is the lowest). A lives on the top floor and B on floor 1. C lives on an even-numbered floor. D lives immediately above E, and E doesn't live on floor 2. Who lives on floor 4?
  42. Six friends sit around a round table facing away from the centre. B is to the immediate left of A. C is opposite A. D is to the immediate right of C. E is not next to A. Who sits next to both A and E?
  43. In a row of 30 children facing north, Tanya is 11th from the right. Arjun is 7th to the left of Tanya. What is Arjun's position from the left?
  44. Rohan ranks 9th from the top and 38th from the bottom in his class. How many students are in the class?
  45. Five cars are parked in a row: a Swift, Creta, Nexon, City and Innova. The City is at one end and the Creta at the other. The Innova is next to the City. The Nexon is immediately between the Swift and the Creta. Which car is in the middle?
  46. In a row, A is 5th from the left and B is 4th from the right. There are 8 people between them, and B is to the right of A. How many people are in the row?
  47. Of five buildings, P is taller than Q but shorter than R. S is taller than R. T is shorter than Q. Which is the second tallest?
  48. Eight people M, N, O, P, Q, R, S and T sit around a round table facing the centre. M is opposite N. O is second to the left of M. P is opposite O. Q is to the immediate right of N. R sits between M and O. S sits next to both N and P. Who sits opposite Q?

Full practice tests

  1. The average of 5 numbers is 42. When one number is removed, the average of the rest is 40. What number was removed?
  2. What is the simple interest on ₹12,000 at 8% a year for 3 years?
  3. What is the compound interest on ₹10,000 at 10% a year for 2 years, compounded annually?
  4. The ratio of Riya's age to her mother's is 2 : 7, and her mother is 25 years older. How old is Riya?
  5. What is the LCM of 36 and 84?
  6. Two coins are tossed. What is the probability of getting at least one head?
  7. What is 20% of 30% of 500?
  8. An article bought for ₹480 is sold at a profit of 12.5%. What is the selling price?
  9. A 150 m train running at 90 km/h passes a pole. How long does it take?
  10. A can finish a job in 8 days and B in 24 days. How long will they take together?
  11. Find the next number: 5, 11, 23, 47, 95, ?
  12. If DOCTOR is coded as EPDUPS, how is NURSE coded?
  13. Pointing to a girl, Raj says, "She is the daughter of the only child of my father." How is Raj related to the girl?
  14. Five people sit in a row facing north. A is to the left of B but to the right of C. D is to the right of B. E is at the left end. Who is in the middle?
  15. A car goes 120 km at 40 km/h and returns at 60 km/h. What is the average speed for the round trip?
  16. ₹7,200 is divided among A, B and C in the ratio 3 : 4 : 5. What is C's share?
  17. Which of these numbers is divisible by 11?
  18. A sum of money doubles in 8 years at simple interest. What is the rate?
  19. A father and son's ages add up to 50. Five years ago, the father was 7 times as old as the son. How old is the son now?
  20. A 60-litre mixture has milk and water in the ratio 2 : 1. How much water must be added to make the ratio 1 : 2?
  21. After a 25% raise, Raj's salary is ₹45,000. What was it before?
  22. An item marked ₹1,600 gets two successive discounts of 10% and 5%. What is the selling price?
  23. A boat's speed in still water is 10 km/h and the stream is 2 km/h. How long does a 48 km trip downstream and back take?
  24. Pipe A fills a tank in 20 minutes and pipe B in 30 minutes. How long do both take together?
  25. Find the next letter: C, F, I, L, ?
  26. A card is drawn from a well-shuffled pack of 52. What is the probability that it is a king or a heart?
  27. In how many ways can the letters of the word INDIA be arranged?
  28. What is the angle between the hands of a clock at 3:30?
  29. 1 January 2024 was a Monday. What day of the week was 1 March 2024?
  30. By selling 20 notebooks, a shopkeeper gains the selling price of 4 notebooks. What is the profit percentage?
  31. What is the average of the first 10 natural numbers?
  32. The average of three numbers is 20. The average of two of them is 15. What is the third number?
  33. What is the difference between compound and simple interest on ₹5,000 at 10% a year for 2 years?
  34. If A : B = 2 : 3 and B : C = 4 : 5, what is A : B : C?
  35. In an election, 10% of voters didn't vote. The winner got 60% of the votes cast and won by 1,800 votes. How many voters were on the list?
  36. Selling a watch for ₹1,440 gives a 20% loss. At what price should it be sold for a 20% profit?
  37. How far does a car at 54 km/h travel in 20 seconds?
  38. 15 workers can finish a job in 12 days. How long will 20 workers take?
  39. Find the next number: 1, 3, 7, 15, 31, ?
  40. Find the next number: 2, 12, 36, 80, 150, ?
  41. If LION = 50 using letter positions, what is TIGER?
  42. A is B's brother. C is A's mother. D is C's father. How is B related to D?
  43. Four friends P, Q, R and S sit around a square table facing the centre. P is opposite R. Q is to the immediate right of P. Who is to the immediate left of P?
  44. A bag has 4 red and 6 blue balls. Two balls are drawn without replacement. What is the probability that both are red?
  45. In how many ways can a team of 3 be chosen from 7 people?
  46. What is the smaller angle between the hands of a clock at 9:15?
  47. 15 August 1947 was a Friday. What day of the week was 15 August 1948?
  48. A's income is 40% more than B's. By what percentage is B's income less than A's?
  49. At what rate of simple interest will ₹8,000 earn ₹1,920 in 3 years?
  50. The average weight of 8 people rises by 2.5 kg when one of them, weighing 65 kg, is replaced by a new person. What does the new person weigh?
  51. A invests ₹40,000 for 12 months and B invests ₹60,000 for 8 months. Out of a profit of ₹18,000, what is A's share?
  52. Rice at ₹40/kg is mixed with rice at ₹60/kg to get a mixture worth ₹52/kg. In what ratio are they mixed?
  53. The present ages of A and B are in the ratio 4 : 5. After 6 years, the ratio will be 5 : 6. What is A's present age?
  54. Two trains start towards each other from stations 300 km apart at 70 km/h and 50 km/h. When do they meet?
  55. What is the unit digit of 7⁹⁵?
  56. If PAPER is coded as QBQFS, how is PENCIL coded?
  57. Introducing Rahul, Anjali says, "His wife is the only daughter of my mother." How is Anjali related to Rahul?
  58. Five people sit in a row facing north. B is second to the right of D. E is at the right end. A sits between D and B. C is to the immediate left of D. Who is at the left end?
  59. A shopkeeper buys 80 kg of rice at ₹40/kg. He sells 50 kg at ₹48/kg and the rest at ₹38/kg. What is his profit percentage?
  60. A 200 m train crosses a 300 m platform in 25 seconds. How long will it take to pass a man walking towards it at 18 km/h?