Interview Q&A / Aptitude

61. What is the difference between compound interest and simple interest on ₹5,000 for 2 years at 8% per annum?

    ₹32. For 2 years the difference is P x (R/100)^2 = 5,000 x 0.08 x 0.08 = ₹32. It is the interest earned in year 2 on year 1's interest.

    BeginnerQuick answer1 min read
62. What is the least number which, when divided by 12, 15, 20 and 54, leaves a remainder of 8 in each case?

    548. The number minus 8 must be a multiple of all four divisors. LCM(12, 15, 20, 54) = 540, so the least such number is 540 + 8 = 548.

    BeginnerQuick answer1 min read
63. What is the next letter in the series A, C, F, J, O, ...?

    U. Using positions A = 1, C = 3, F = 6, J = 10, O = 15, the gaps are 2, 3, 4, 5, so the next gap is 6 and the next position is 21, which is U.

    BeginnerQuick answer1 min read
64. What is the next number in the series 2, 3, 5, 9, 17, ...?

    33. The differences are 1, 2, 4, 8, which double each time, so the next difference is 16 and 17 + 16 = 33. Each term is also 2^n + 1, or double the previous term minus 1.

    BeginnerQuick answer1 min read
65. What is the next term in the series 4, 9, 25, 49, 121, ...?

    169. The terms are squares of consecutive prime numbers: 2^2, 3^2, 5^2, 7^2, 11^2, so the next is 13^2 = 169.

    BeginnerQuick answer1 min read
66. What is the probability that a randomly chosen leap year has 53 Sundays?

    2/7. A leap year has 366 days = 52 weeks + 2 extra days. Those 2 consecutive days can be any of 7 pairs (Mon-Tue, ..., Sun-Mon), and 2 of them include a Sunday.

    BeginnerQuick answer1 min read
67. What is the unit digit of 7^95?

    The answer is 3. Unit digits of powers of 7 repeat in a cycle of four (7, 9, 3, 1). 95 leaves remainder 3 when divided by 4, so 7^95 ends like 7^3, which ends in 3.

    BeginnerQuick answer1 min read
68. ₹10,000 is lent partly at 8% and partly at 12% simple interest. The total interest for one year is ₹960. How much was lent at each rate?

    ₹6,000 at 8% and ₹4,000 at 12%. The overall rate is 960/10,000 = 9.6%. Alligation gives (12 - 9.6) : (9.6 - 8) = 2.4 : 1.6 = 3 : 2.

    IntermediateQuick answer1 min read
69. A bag has ₹1, 50-paise and 25-paise coins in the ratio 5 : 6 : 8, worth ₹210 in total. How many coins of each kind are there?

    105 one-rupee, 126 fifty-paise and 168 twenty-five-paise coins. Take counts 5x, 6x, 8x. Their value is 5x + 3x + 2x = 10x rupees = 210, so x = 21.

    IntermediateQuick answer1 min read
70. A boat takes twice as long to go upstream as to cover the same distance downstream. What is the ratio of the boat's speed in still water to the speed of the stream?

    3 : 1. Same distance and double the time means the downstream speed is twice the upstream speed: b + s = 2(b - s), so b = 3s.

    IntermediateQuick answer1 min read
71. A can do a job in 20 days. A works alone for 4 days, then B joins and together they finish the rest in 6 days. How long would B take alone?

    12 days. A works all 10 days and does 10/20 = half the job. B does the other half in 6 days, so B alone would need 12 days.

    IntermediateQuick answer1 min read
72. A can finish a job in 6 days and B in 12 days. If they work on alternate days, starting with A, in how many days will the job be finished?

    8 days. With 12 units of work, A does 2 units a day and B 1. Every 2-day cycle does 3 units, so 4 cycles (8 days) finish exactly 12 units.

    IntermediateQuick answer1 min read
73. A milkman buys milk at ₹60 per litre. How much water should he add per litre so that by selling the mixture at ₹60 per litre he makes a 20% profit?

    200 ml per litre (milk : water = 5 : 1). For 20% profit at ₹60, the mixture's cost must be 60 / 1.2 = ₹50 per litre. Alligation of milk (₹60) and water (₹0) about ₹50 gives 50 : 10 = 5 : 1.

    IntermediateQuick answer1 min read
74. A sells a bicycle to B at a 20% profit, and B sells it to C at a 25% profit. If C pays ₹1,500, what did A pay for it?

    ₹1,000. Each sale multiplies the price: CP of A x 1.2 x 1.25 = 1,500, so A's cost = 1,500 / 1.5 = ₹1,000.

    IntermediateQuick answer1 min read
75. A sum at compound interest amounts to ₹6,050 in 2 years and ₹6,655 in 3 years. Find the rate and the principal.

    Rate = 10% and principal = ₹5,000. The third year's interest is 6,655 - 6,050 = ₹605, which is 10% of ₹6,050. Then P = 6,050 / (1.1)^2 = 6,050 / 1.21 = ₹5,000.

    IntermediateQuick answer1 min read
76. At what time between 4 and 5 o'clock are the hands of a clock together?

    At 21 9/11 minutes past 4 (about 4:21:49). At 4:00 the minute hand is 120 degrees behind, and it gains 5.5 degrees a minute, so it catches up in 120/5.5 = 240/11 = 21 9/11 minutes.

    IntermediateQuick answer1 min read
77. Find the greatest number that divides 43, 91 and 183 leaving the same remainder in each case.

    The answer is 4. If a number leaves the same remainder for all three, it divides their differences exactly: 48, 92 and 140. HCF(48, 92, 140) = 4, and indeed each number leaves remainder 3 when divided by 4.

    IntermediateQuick answer1 min read
78. How do you quickly approximate a value like '3,487 is what percent of 15,012?' in a timed data interpretation section?

    Round both numbers to friendly values close to the originals: 3,500 / 15,000 = 7/30, about 23.3%. The exact value is 23.23%, so the estimate is enough to pick the right option when choices are reasonably far apart.

    IntermediateQuick answer1 min read
79. How many factors does 360 have, and what is the sum of those factors?

    Write 360 = 2^3 x 3^2 x 5. Number of factors = (3+1)(2+1)(1+1) = 24. Sum of factors = (1+2+4+8)(1+3+9)(1+5) = 15 x 13 x 6 = 1170.

    IntermediateQuick answer1 min read
80. If a boy walks to school at 5 km/h he is 7 minutes late; at 6 km/h he is 5 minutes early. How far is the school?

    6 km. The two journey times differ by 7 + 5 = 12 minutes = 1/5 hour. So d/5 - d/6 = 1/5, which gives d/30 = 1/5 and d = 6 km.

    IntermediateQuick answer1 min read
81. If DELHI is coded as 73541 and CALCUTTA as 82589662, how is CALICUT coded?

    8251896. Each letter has a fixed digit: D 7, E 3, L 5, H 4, I 1, C 8, A 2, U 9, T 6. So C-A-L-I-C-U-T becomes 8-2-5-1-8-9-6.

    IntermediateQuick answer1 min read
82. If P + Q means P is the father of Q, P - Q means P is the wife of Q, and P x Q means P is the brother of Q, what does A - B + C x D mean about A and D?

    A is D's mother. A - B: A is B's wife. B + C: B is C's father. C x D: C is D's brother, so D is also B's child. Since A is B's wife, A is the mother of D.

    IntermediateQuick answer1 min read
83. In a 1 km race, A beats B by 100 m and B beats C by 100 m. By how many metres does A beat C?

    190 m. When A runs 1,000 m, B runs 900 m. When B runs 1,000 m, C runs 900 m, so when B runs 900 m, C runs 810 m. Hence A beats C by 1,000 - 810 = 190 m.

    IntermediateQuick answer1 min read
84. In a code language, 'pit dar na' means 'you are good', 'dar tok pa' means 'good and bad' and 'kim na tok' means 'boys are bad'. What are the codes for 'and' and 'you'?

    and' is pa and 'you' is pit. Common words and common codes match up: good = dar (sentences 1 and 2), bad = tok (2 and 3), are = na (1 and 3). Removing those leaves pa for 'and' and pit for 'you'.

    IntermediateQuick answer1 min read
85. In how many ways can 6 people sit around a round table? In how many of these do two particular friends sit together?

    120 ways in total, since circular arrangements of n people number (n - 1)! = 5! = 120. With two friends together, treat them as one unit: (5 - 1)! x 2 = 24 x 2 = 48 ways.

    IntermediateQuick answer1 min read
86. In how many ways can the letters of LEADER be arranged so that the vowels always come together?

    72. Treat the vowels E, A, E as one block. The block plus L, D, R makes 4 units, arranged in 4! = 24 ways. Inside the block, E, A, E arrange in 3!/2! = 3 ways. Total 24 x 3 = 72.

    IntermediateQuick answer1 min read
87. Pipes A and B can fill a tank in 20 and 30 minutes. Both are opened, and after 5 minutes B is closed. How much longer does A take to fill the tank?

    11 minutes 40 seconds. With 60 units: together they add 5 units a minute, so 25 units in 5 minutes. A then fills the remaining 35 units at 3 a minute, taking 35/3 = 11 2/3 minutes.

    IntermediateQuick answer1 min read
88. Plant A produced 450, 520 and 600 units over three years, and Plant B produced 300, 390 and 480 units. What is B's total output as a percentage of A's, and in which year was B's output closest to A's?

    B's total (1,170) is about 74.52% of A's total (1,570). Year by year, B/A is 66.7%, 75% and 80%, so B came closest to A in the third year, even though the gap in units (120) was smallest in the first and third years.

    IntermediateQuick answer1 min read
89. Six people P, Q, R, S, T and U sit around a round table facing the centre. P is opposite S. Q is immediately to the left of P. T is opposite Q. U is not next to S. Who is opposite R, and who sits between Q and S?

    U is opposite R, and R sits between Q and S. When people face the centre, a person's left is the next seat clockwise. Clockwise from P the order is P, Q, R, S, T, U.

    IntermediateQuick answer1 min read
90. Ten years ago, A was half as old as B. If the ratio of their present ages is 3 : 4, what is the sum of their present ages?

    35 years. Present ages 3x and 4x. Ten years ago: 3x - 10 = (4x - 10)/2, so 6x - 20 = 4x - 10 and x = 5. Ages are 15 and 20.

    IntermediateQuick answer1 min read