Interview Q&A / Aptitude

1. How do you calculate successive percentage changes?

   Two changes of a% and b% give a net change of a + b + (a x b) / 100 percent. Use negative values for decreases. For example, a 20% increase followed by a 20% decrease is a net 4% decrease, not zero.

   BeginnerIn-depth3 min read
2. How do you solve profit and loss questions with marked price and discount?

   Profit or loss percent is always calculated on the cost price. Discount percent is always calculated on the marked price. Chain them with multipliers. For example, mark up 25% and give 10% off, and the selling price is 1.25 x 0.9 = 1.125 times the cost, which is a 12.5% profit.

   BeginnerIn-depth4 min read
3. How do you solve ratio and age problems?

   Write the present ages as multiples of one unknown using the given ratio, such as 4x and 5x, then add or subtract the same number of years to both and set up an equation from the second condition. Both people age by the same amount, so the difference between their ages never changes.

   BeginnerIn-depth4 min read
4. How do you solve time and work problems quickly?

   Convert each person's time into work per day (1 divided by days), add rates when people work together, and divide total work by the combined rate. The LCM method makes it faster. Take total work as the LCM of the days, so each rate becomes a whole number.

   BeginnerIn-depth3 min read
5. What is the difference between simple interest and compound interest?

   Simple interest is calculated only on the original principal, so it is the same every year (SI = P x R x T / 100). Compound interest is calculated on the principal plus the interest already earned, so it grows every year (A = P x (1 + R/100)^T). For 2 years, the difference is P x (R/100)^2.

   BeginnerIn-depth4 min read
6. How do you solve probability questions on coins, dice and cards?

   Probability = favourable outcomes / total outcomes, when all outcomes are equally likely. List the sample space carefully. Two coins have 4 outcomes, two dice have 36, a deck has 52 cards. For "at least one" questions, use 1 minus the probability of none.

   IntermediateIn-depth4 min read
7. How do you solve speed, distance and time questions, including trains and relative speed?

   Use distance = speed x time and convert km/h to m/s by multiplying by 5/18. A train crossing a pole covers its own length; crossing a platform or another train covers both lengths. Add speeds when objects move in opposite directions and subtract when they move in the same direction.

   IntermediateIn-depth4 min read
8. What is the difference between permutations and combinations, and how do you know which to use?

   Use permutations when order matters, like choosing a captain and vice-captain, and combinations when order does not matter, like choosing a committee. nPr = n! / (n - r)! and nCr = n! / (r! x (n - r)!). Each combination of r items can be arranged in r! ways, so nPr = nCr x r!.

   AdvancedIn-depth4 min read
9. 12 men can finish a job in 18 days working 8 hours a day. How many days will 16 men take working 9 hours a day?

   12 days. Total work in man-hours = 12 x 18 x 8 = 1,728. With 16 men at 9 hours a day, daily output = 144 man-hours, so days = 1,728 / 144 = 12.

   BeginnerQuick answer1 min read
10. A 60-litre mixture has alcohol and water in the ratio 2 : 1. How much water must be added to make the ratio 1 : 2?

    60 litres. The mixture has 40 L alcohol and 20 L water. Alcohol stays 40 L, and for 1 : 2 water must be 80 L. So add 80 - 20 = 60 litres of water.

    BeginnerQuick answer1 min read
11. A and B together finish a job in 12 days. B alone takes 30 days. How long does A take alone?

    20 days. A's daily work = together minus B = 1/12 - 1/30 = (5 - 2)/60 = 3/60 = 1/20. With total work 60 units: together 5 units a day, B 2, so A does 3 units a day and needs 60/3 = 20 days.

    BeginnerQuick answer1 min read
12. A bag has 5 red and 3 blue balls. Two balls are drawn at random without replacement. What is the probability that both are red?

    5/14. First red: 5/8. Second red, given the first was red: 4/7. Multiply: 5/8 x 4/7 = 20/56 = 5/14. Using combinations: C(5,2)/C(8,2) = 10/28 = 5/14.

    BeginnerQuick answer1 min read
13. A batsman scores 85 runs in his 17th innings and his average goes up by 3. What is his average after the 17th innings?

    37. If the old average was a, then 16a + 85 = 17(a + 3), so a = 34 and the new average is 37. Quick view: 85 covers the new average once plus 3 extra for each of the 16 earlier innings, so new average = 85 - 16 x 3 = 37.

    BeginnerQuick answer1 min read
14. A boat goes downstream at 15 km/h and upstream at 9 km/h. What are the speed of the boat in still water and the speed of the stream?

    Boat 12 km/h and stream 3 km/h. Downstream = b + s and upstream = b - s, so b = (15 + 9)/2 = 12 and s = (15 - 9)/2 = 3.

    BeginnerQuick answer1 min read
15. A car travels for the first half of the journey's time at 50 km/h and the second half of the time at 70 km/h. What is its average speed?

    60 km/h. When the time intervals are equal, the average speed is the simple average of the speeds: (50 + 70)/2 = 60. For example, 1 hour at 50 and 1 hour at 70 covers 120 km in 2 hours.

    BeginnerQuick answer1 min read
16. A company's sales (in ₹ crore) were 120 in 2021, 150 in 2022, 180 in 2023, 165 in 2024 and 210 in 2025. In which year was the percentage growth over the previous year highest, and what was the average sales figure?

    2025, with 27.27% growth (45 on 165). Growth was 25% in 2022, 20% in 2023 and -8.33% in 2024. The average sales over the five years is 825 / 5 = ₹165 crore.

    BeginnerQuick answer1 min read
17. A family's monthly budget of ₹60,000 is shown in a pie chart: rent 30%, food 25%, transport 10%, savings 20%, others 15%. What is the central angle for food, and how much more is spent on rent than saved?

    Food's angle is 25% of 360 = 90 degrees. Rent is ₹18,000 and savings ₹12,000, so rent exceeds savings by ₹6,000. In general, angle = percent x 3.6, and amount = percent x total / 100.

    BeginnerQuick answer1 min read
18. A father is three times as old as his son. In 15 years he will be twice as old as his son. What are their present ages?

    Son 15, father 45. Let the son be x and the father 3x. In 15 years: 3x + 15 = 2(x + 15), so x = 15.

    BeginnerQuick answer1 min read
19. A hits a target 3 times in 5 shots and B hits it 2 times in 4 shots. If both fire once, what is the probability that the target is hit?

    4/5. P(A hits) = 3/5, P(B hits) = 1/2. The target is missed only if both miss: 2/5 x 1/2 = 1/5. So P(hit) = 1 - 1/5 = 4/5.

    BeginnerQuick answer1 min read
20. A invests ₹40,000 for 12 months and B invests ₹50,000 for 6 months. How should a profit of ₹39,000 be shared?

    In the ratio of capital x time: 40,000 x 12 : 50,000 x 6 = 4,80,000 : 3,00,000 = 8 : 5. So A gets 39,000 x 8/13 = ₹24,000 and B gets ₹15,000.

    BeginnerQuick answer1 min read
21. A is the sister of B. C is B's mother. D is C's father. E is D's mother. How is A related to D, and to E?

    A is D's granddaughter and E's great-granddaughter. A and B are children of C; C is D's child, so A is D's grandchild, and A is female (a sister), so granddaughter. D is E's son, so A is E's great-granddaughter.

    BeginnerQuick answer1 min read
22. A man faces north. He turns 90 degrees clockwise and then 135 degrees anticlockwise. Which direction is he facing now?

    North-west. Net rotation = 90 clockwise - 135 anticlockwise = 45 degrees anticlockwise from north, which is north-west.

    BeginnerQuick answer1 min read
23. A man sells a watch for ₹1,140 and loses 5%. At what price should he sell it to gain 5%?

    ₹1,260. ₹1,140 is 95% of cost, so cost = 1,140 / 0.95 = ₹1,200. To gain 5%, sell at 1.05 x 1,200 = ₹1,260. Directly: 1,140 x 105/95 = 1,260.

    BeginnerQuick answer1 min read
24. A number is picked at random from 1 to 50. What is the probability that it is divisible by 3 or 5?

    23/50. Multiples of 3: 16. Multiples of 5: 10. Multiples of both (15, 30, 45): 3. By inclusion-exclusion, 16 + 10 - 3 = 23 favourable numbers out of 50.

    BeginnerQuick answer1 min read
25. A person travels from Pune to Mumbai at 60 km/h and returns at 40 km/h. What is the average speed for the whole trip?

    48 km/h, not 50. For equal distances the average speed is the harmonic mean: 2 x 60 x 40 / (60 + 40) = 4,800 / 100 = 48 km/h, because more time is spent at the slower speed.

    BeginnerQuick answer1 min read
26. A pipe fills a tank in 10 hours, but a leak at the bottom can empty the full tank in 15 hours. With both working, how long does the tank take to fill?

    30 hours. Net rate = 1/10 - 1/15 = (3 - 2)/30 = 1/30 of the tank per hour. With 30 units: the pipe adds 3, the leak removes 2, net 1 unit per hour.

    BeginnerQuick answer1 min read
27. A pipe normally fills a tank in 8 hours, but because of a leak it takes 10 hours. How long would the leak take to empty a full tank?

    40 hours. Leak rate = normal rate - actual rate = 1/8 - 1/10 = 1/40 of the tank per hour. With 40 units: the pipe adds 5, the net is 4, so the leak removes 1 unit per hour.

    BeginnerQuick answer1 min read
28. A shopkeeper sells rice at cost price but uses a 900 g weight instead of 1 kg. What is his profit percentage?

    11.11% (11 1/9 %). He charges for 1,000 g but hands over 900 g, gaining 100 g on every 900 g he actually gives. Profit % = 100/900 x 100 = 11.11%.

    BeginnerQuick answer1 min read
29. A student needs 40% to pass. She scores 178 marks and fails by 22 marks. What are the maximum marks?

    500. Pass marks = 178 + 22 = 200, and 200 is 40% of the maximum, so maximum = 200 / 0.40 = 500.

    BeginnerQuick answer1 min read
30. A sum at simple interest amounts to ₹7,200 in 2 years and ₹8,400 in 4 years. Find the principal and the rate.

    Principal ₹6,000 and rate 10% per year. Two extra years added ₹1,200, so yearly interest is ₹600. Two years of interest is ₹1,200, so P = 7,200 - 1,200 = ₹6,000, and R = 600/6,000 = 10%.

    BeginnerQuick answer1 min read