Interview Q&A / Aptitude

1. If A : B = 2 : 3 and B : C = 4 : 5, what is A : B : C?

   8 : 12 : 15. Make the common term B equal in both ratios. B is 3 in the first and 4 in the second, so scale the first by 4 and the second by 3: A : B = 8 : 12 and B : C = 12 : 15.

   BeginnerQuick answer1 min read
2. Two numbers are in the ratio 3 : 5. If 9 is added to each, the ratio becomes 3 : 4. Find the numbers.

   9 and 15. Let them be 3x and 5x. Then (3x + 9)/(5x + 9) = 3/4, so 12x + 36 = 15x + 27, giving x = 3. The numbers are 9 and 15, and 18 : 24 is indeed 3 : 4.

   BeginnerQuick answer1 min read
3. What are the fourth proportional, third proportional and mean proportional, with an example of each?

   For a : b = c : d, d is the fourth proportional, d = bc/a (4, 9, 12 gives 27). For a : b = b : c, c is the third proportional, c = b^2/a (4, 6 gives 9). The mean proportional between a and b is the square root of ab (9 and 16 give 12).

   BeginnerQuick answer1 min read
4. 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
5. 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