Question 17

Given below are two statements :
Statement I: The ratio of the son's age to the father's age is 1 : 5. The product of their ages is 245. The ratio of the son's age to the father's age after 9 years will be 3 : 5.
Statement II: A milkman adds 30 litres of water to 70 litres of milk. After selling 1/5th of the total quantity, he adds water equal to the quantity he sold. The proportion of water to milk he sells now would be 28 : 72.
In the light of the above statements, choose the correct answer from the options given below.

Solution

Statement I:

It is given that the ratio of son's age to father's age is 1:5

Let the son's age be x and father's age be 5x.

(x)(5x) = 245

x = 7

Therefore, son's age is 7 years and father's age is 35 years.

After 9 years, son's age is 16 years and father's age is 44 years.

Ratio = 16 : 44 = 4 : 11

Statement II:

Initially - 70L milk and 30L water

After selling 1/5th of the solution - 56L milk and 24L water

Adding water - 56L milk and 44L water

water:milk = 44:56 = 11:14

The answer is option B.

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