Interview Q&A / Aptitude

91. The average age of 8 men rises by 2 years when two of them, aged 21 and 23, are replaced by two women. What is the average age of the women?

    30 years. The group's total rises by 8 x 2 = 16 years. So the women together are 21 + 23 + 16 = 60 years, an average of 30.

    IntermediateQuick answer1 min read
92. The incomes of two people are in the ratio 4 : 3 and their expenses in the ratio 3 : 2. If each saves ₹6,000 a month, what are their incomes?

    ₹24,000 and ₹18,000. With incomes 4x, 3x and expenses 3y, 2y: 4x - 3y = 6,000 and 3x - 2y = 6,000. Solving gives x = 6,000 and y = 6,000.

    IntermediateQuick answer1 min read
93. Two phones are each sold for ₹1,200, one at a 20% profit and the other at a 20% loss. What is the overall profit or loss?

    An overall loss of 4%, or ₹100. Costs are 1,200/1.2 = ₹1,000 and 1,200/0.8 = ₹1,500. Total cost ₹2,500, total sale ₹2,400. When selling prices are equal and the gain and loss percentages are equal, there is always a loss of x^2/100 %.

    IntermediateQuick answer1 min read
94. Two pipes fill a cistern in 36 and 45 minutes. A waste pipe can empty it in 30 minutes. If all three are opened together, how long does the cistern take to fill?

    60 minutes. With 180 units: the inlets add 5 and 4 a minute and the waste pipe removes 6, so the net is 3 units a minute and 180/3 = 60 minutes.

    IntermediateQuick answer1 min read
95. What is the largest square tile that can pave a floor 15 m 17 cm long and 9 m 2 cm wide, and how many such tiles are needed?

    Convert to centimetres: 1517 and 902. HCF(1517, 902) = 41, so the largest tile is 41 cm by 41 cm. Tiles needed = (1517/41) x (902/41) = 37 x 22 = 814.

    IntermediateQuick answer1 min read
96. What is the remainder when 2^100 is divided by 7?

    The remainder is 2. Since 2^3 = 8 leaves remainder 1 when divided by 7, 2^99 = (2^3)^33 also leaves 1, so 2^100 = 2^99 x 2 leaves 1 x 2 = 2.

    IntermediateQuick answer1 min read
97. What is the rule of 72, and how long does money take to double at 9% compound interest?

    Doubling time is roughly 72 divided by the annual rate in percent. At 9% that is 72 / 9 = 8 years. The exact answer is log 2 / log 1.09, about 8.04 years, so the rule is very close.

    IntermediateQuick answer1 min read
98. Which is the next year after 2025 that will have exactly the same calendar as 2025?

    2031. Two years share a calendar when they start on the same weekday and are both leap or both non-leap. Adding odd days from 2025 onward (1, 1, 1, 2, 1, 1) reaches 7 after 2030, so 2031 starts on the same day as 2025 (Wednesday) and is also a non-leap year.

    IntermediateQuick answer1 min read
99. A 40-litre can is full of milk. 4 litres are taken out and replaced with water, and this is done three times in total. How much milk is left?

    29.16 litres. Each operation keeps (40 - 4)/40 = 0.9 of the milk, so after three rounds milk = 40 x 0.9^3 = 40 x 0.729 = 29.16 litres.

    AdvancedQuick answer1 min read
100. A boat's speed in still water is 15 km/h. It goes 30 km upstream and returns in 4 hours 30 minutes. What is the speed of the stream?

     5 km/h. Solve 30/(15 - s) + 30/(15 + s) = 4.5. This gives 900/(225 - s^2) = 4.5, so 225 - s^2 = 200 and s = 5. Check: 30/10 + 30/20 = 3 + 1.5 = 4.5 hours.

     AdvancedQuick answer1 min read
101. How do you find the HCF and LCM of fractions such as 2/3, 8/9 and 16/81?

     HCF of fractions = HCF of numerators / LCM of denominators; LCM of fractions = LCM of numerators / HCF of denominators. For 2/3, 8/9, 16/81 the HCF is 2/81 and the LCM is 16/3.

     AdvancedQuick answer1 min read
102. In how many ways can 5 boys and 3 girls stand in a row so that no two girls are next to each other?

     14,400. Arrange the boys first: 5! = 120. They create 6 gaps (including the two ends). Choose and fill 3 of those gaps with the girls in order: 6 x 5 x 4 = 120. Total 120 x 120 = 14,400.

     AdvancedQuick answer1 min read
103. In how many ways can a committee of 5 be formed from 6 men and 4 women so that it has at least 2 women?

     186. Total committees C(10,5) = 252. Subtract those with no woman, C(6,5) = 6, and with exactly one woman, 4 x C(6,4) = 60. 252 - 66 = 186.

     AdvancedQuick answer1 min read
104. Ravi spends 75% of his income. His income rises by 20% and his spending by 10%. By what percentage do his savings increase?

     By 50%. Take income 100, spending 75, savings 25. New income 120, new spending 82.5, new savings 37.5. Increase = 12.5 on 25 = 50%.

     AdvancedQuick answer1 min read
105. Statements: All roses are flowers. Some flowers are red. Conclusions: I. Some roses are red. II. No rose is red. Which follows?

     Either I or II follows. Neither is certain on its own, but they are a complementary pair about the same two terms: one of 'some roses are red' and 'no rose is red' must be true. So the answer is 'either I or II'.

     AdvancedQuick answer1 min read
106. The minute hand of a clock overtakes the hour hand every 64 minutes of correct time. How much does the clock gain or lose in a day?

     It gains 32 8/11 minutes a day. In a correct clock the hands meet every 65 5/11 minutes. Here they meet after only 64 real minutes, so the clock runs fast: it shows 65 5/11 minutes in 64 real minutes, gaining 16/11 minutes every 64 minutes, which is 360/11 = 32 8/11 minutes in 1,440 minutes.

     AdvancedQuick answer1 min read
107. What day of the week was 15 August 1947?

     Friday. Count odd days (days beyond complete weeks): 1,900 years give 1 odd day, 1901 to 1946 give 46 + 11 leap days = 57, which is 1, and 1 January to 15 August 1947 gives 227 days, which is 3. Total 5 odd days, and 5 corresponds to Friday.

     AdvancedQuick answer1 min read
108. What is the probability that 4 randomly chosen people were all born on different days of the week?

     840/2401, about 0.35. The first person can be born on any day (7/7), the second on one of 6 other days, the third on 5, the fourth on 4: (7 x 6 x 5 x 4) / 7^4 = 840/2401.

     AdvancedQuick answer1 min read