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Question

(D) Let Ram's present age be $R$, his son's age be $S$, and his father's age be $F$.According to the problem, $R = 3S$, which implies $S = \frac{R}{3}

Vedclass · Accepted Answer

$78$

Vedclass · Answer

(D) Let Ram's present age be $R$, his son's age be $S$, and his father's age be $F$.According to the problem, $R = 3S$, which implies $S = \frac{R}{3}$.Also, $R = \frac{2}{5}F$, which implies $F = \frac{5R}{2}$.The average of their ages is given as $46 \, 	ext{years}$, so $\frac{R + S + F}{3} = 46$.This gives $R + S + F = 138$.Substituting the values of $S$ and $F$ in terms of $R$: $R + \frac{R}{3} + \frac{5R}{2} = 138$.Multiplying by $6$ to clear the denominators: $6R + 2R + 15R = 138 	imes 6$.$23R = 828$, so $R = \frac{828}{23} = 36$.Now, $S = \frac{36}{3} = 12 \, 	ext{years}$ and $F = \frac{5 	imes 36}{2} = 90 \, 	ext{years}$.The difference between the son's age and the father's age is $F - S = 90 - 12 = 78 \, 	ext{years}$.

Ram's present age is three times his son's present age and $\frac{2}{5}$ of his father's present age. The average of the present ages of all of them is $46 \, \text{years}$. What is the difference between the Ram's son's present age and Ram's father's present age? (in $\text{years}$)

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