The sum of the present ages of a father and h | vedclass

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Question

(C) Let the present age of the father be $F$ and the son be $S$.Given that the sum of their present ages is $90$ years: $F + S = 90$ (Equation $1$).$1

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(C) Let the present age of the father be $F$ and the son be $S$.Given that the sum of their present ages is $90$ years: $F + S = 90$ (Equation $1$).$10$ years ago,the father's age was $(F - 10)$ and the son's age was $(S - 10)$.The ratio of their ages $10$ years ago was $5:2$,so: $\frac{F - 10}{S - 10} = \frac{5}{2}$.Cross-multiplying gives: $2(F - 10) = 5(S - 10) \Rightarrow 2F - 20 = 5S - 50 \Rightarrow 2F - 5S = -30$ (Equation $2$).From Equation $1$,$S = 90 - F$. Substituting this into Equation $2$:$2F - 5(90 - F) = -30$$2F - 450 + 5F = -30$$7F = 420$$F = 60$.Therefore,the present age of the father is $60$ years.

The sum of the present ages of a father and his son is $90$ years. $10$ years ago,the ratio of their ages was $5:2$. The present age of the father is (in years):

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