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One year ago a father was four times as old as his son .after 6 year his age exceed than twice of his son age by 9 year. Ratio of their present age is what

A.

30 yrs.

B.

33 yrs.

C.

20 yrs

D.

11 yrs

Answer with explanation

Answer: Option BExplanation

Lets denote the ages of the man and his son as M and S respectively.

One year ago their ages were M – 1 and S – 1 respectively.

So from the first statement, M – 1 = 4 * (S – 1) or

M – 4*S = -3 ← Equation 1

In 6 years time both would be older by 6 years, or M+6 and S+6.

From the second statement,

M + 6 = 2 * (S +6) + 9, or

M – 2*S = 15 ← Equation 2

Subtracting Equation 1 from Equation 2, we get:

M – 2*S – (M – 4*S) = 15 – (-3)

That is, 2*S = 18 , or S = 9. Therefore the Son’s present age is 9.

From Equation 2, M = 15 + 2*S or M = 15 + 18 = 33.

Therefore the Father’s present age is 33.

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