If 4 , text{years} ago the ratio between the | vedclass

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(B) Let the present ages of $P$ and $Q$ be $P$ and $Q$ respectively.According to the problem, $4 \, 	ext{years}$ ago, their ages were $(P-4)$ and $(Q

Vedclass · Accepted Answer

$6:7$

Vedclass · Answer

(B) Let the present ages of $P$ and $Q$ be $P$ and $Q$ respectively.According to the problem, $4 \, 	ext{years}$ ago, their ages were $(P-4)$ and $(Q-4)$.The ratio was given as $\frac{P-4}{Q-4} = \frac{5}{6}$.Cross-multiplying gives $6(P-4) = 5(Q-4)$, which simplifies to $6P - 24 = 5Q - 20$, or $6P - 5Q = 4 \quad (1)$.We are also given that the sum of their present ages is $52$, so $P + Q = 52$, which means $P = 52 - Q \quad (2)$.Substituting $(2)$ into $(1)$: $6(52 - Q) - 5Q = 4$.$312 - 6Q - 5Q = 4$.$312 - 11Q = 4$.$11Q = 308$.$Q = 28$.Now, find $P$: $P = 52 - 28 = 24$.The ratio of their present ages is $P:Q = 24:28$.Dividing both by $4$, we get $6:7$.

If $4 \, \text{years}$ ago the ratio between the ages of $P$ and $Q$ was $5:6$ and the sum of their ages at present is $52 \, \text{years}$, what is the ratio of their present ages?

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