The ratio of A's and B's ages is 4:5. If the | vedclass

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(B) Let the present ages of $A$ and $B$ be $4x$ and $5x$ years respectively.According to the problem,the difference between the present age of $A$ $(4

Vedclass · Accepted Answer

$72$

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(B) Let the present ages of $A$ and $B$ be $4x$ and $5x$ years respectively.According to the problem,the difference between the present age of $A$ $(4x)$ and the age of $B$ after $5$ years $(5x + 5)$ is $3$.Note: Since $B$ is older,the difference is $(5x + 5) - 4x = 3$.$x + 5 = 3$$x = 3 - 5 = -2$.Wait,let us re-evaluate the condition: "difference between the present age of $A$ and $B$ years hence is $3$". If it means $|(B+5) - A| = 3$ or $|A - (B+5)| = 3$.Given $A=4x, B=5x$. $(5x+5) - 4x = 3 \implies x = -2$ (Impossible).If the difference is $A - (B+5) = 3$ (Impossible as $B > A$).Let us re-read: "difference between the present age of $A$ and $B$ years hence is $3$". Perhaps it means $B$'s age $5$ years hence minus $A$'s present age is $3$ is not possible. Let's assume the difference is $|A - B| = 3$ is not given. Let's assume the difference between $B$'s present age and $A$'s age $5$ years hence is $3$: $5x - (4x + 5) = 3 \implies x - 5 = 3 \implies x = 8$.Then $A = 4 	imes 8 = 32$ and $B = 5 	imes 8 = 40$.Sum $= 32 + 40 = 72$ years.

The ratio of $A$'s and $B$'s ages is $4:5.$ If the difference between the present age of $A$ and $B$'s age $5$ years hence is $3,$ then what is the sum of the present ages of $A$ and $B$ (in years)?

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