The questions in this article are taken to bring you the standard style of questions on ratios. Such questions form a part of the exams that are usually considered a shade below CAT.
Problem 1: The head of a fish is 6 inches long. Its tail is as long as its head and half its body. If its body is half of its whole length, how long is the fish?
[1] 16 inches
[2] 24 inches
[3] 32 inches
[4] 48 inches
Solution:
Given, tail T = H+B/2 , where H is the head and B is the body.
Also, B = L/2 , where L is the whole length.
Here, whole length L= H+B+T
[Substituting from above]
Hence, the correct choice is [4].
Problem 2:
There are 3 cars moving at speeds in the ratio of . If the fastest car covers 10 km more than the car with medium speed in 30 minutes, then the speed of the slowest car in kmph is:
[1] 30 kmph
[2] 60 kmph
[3] 75 kmph
[4] 100 kmph
Solution:
Let the speeds of the three cars be 1.5y kmph, 2.5y kmph, and 3y kmph.
The fastest car, then, covers 3y/2 km in 30 minutes.
Therefore, the speed of the slowest car is (1.5 × 40) = 60 kmph.
Hence, choice [2] is the answer.
Problem 3:
A bartender has two casks full of mixture of vodka and tomato juice. The ratio of vodka and tomato juice in the first and second cask is 3:10 and 8:15 respectively. In what proportion should the mixtures be mixed to satisfy a customer who likes vodka and tomato juice in the ratio 7:16?
[1] 1 : 2
[2] 117 : 213
[3] 13 : 22
[4] 2 : 3
Solution:
You should note the total amounts of mixtures in both the casks and then use the ratios to form the solution of such problems.
Let the ratio of the mixtures from the two casks be mixed in the ratio x: y to achieve the final ratio of 7:16 for the customer.
Understanding the above equation is important for subsequent questions on ratios, so spend some time on it if you have difficulty forming the above equation.
Solving, we get:
1104x+1664y=1610x+1365y or 506x = 299y or x : y = 299: 506 = 13: 22
Hence, choice [3] is three is the answer.
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