The combined ages of a man and his son are 60 years. Twelve years ago, the father was five times as old as his son. Then their present ages are?

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42 and 18

50 and 10

48 and 12

40 and 20

answer is A.

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Detailed Solution

Let us assume that the present age of the father and the son is x years and y years respectively. We are given that the combined ages of the father and the son are 60 years. So, we get the following equation,
x + y = 60...........(1)
We are also given that twelve years ago, the father was five times as old as his son. Twelve years ago, the age of the father was x − 12 and the age of the son was y − 12. So, we get the following equation,
x – 12 = 5(y − 12)…......(2)
Now, we have two linear equations in two variables. We will use the substitution method to find the values of x and y. From equation (1), we will substitute x = 60 − y in equation (2) in the following manner,
60 – y – 12 = 5(y − 12)
Simplifying the above equation, we get
48 – y = 5y – 60
⇒ 48 + 60 = 5y + y
⇒108 = 6y
∴y = 18
Now, substituting the value of y in equation (1), we get
x + 18 = 60
⇒ x = 60 – 18
∴x = 42
Hence, the present ages of the father and the son are 42 years and 18 years respectively.

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