The ratio of ages between A and B is 6: 5 and | vedclass

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Question

(A) Given the ratio $A:B = 6:5$,we can write $B = \frac{5}{6}A$.Given $B:E = 2:3$,we can write $E = \frac{3}{2}B = \frac{3}{2} 	imes \frac{5}{6}A = \

Vedclass · Accepted Answer

$12: 11$

Vedclass · Answer

(A) Given the ratio $A:B = 6:5$,we can write $B = \frac{5}{6}A$.Given $B:E = 2:3$,we can write $E = \frac{3}{2}B = \frac{3}{2} 	imes \frac{5}{6}A = \frac{5}{4}A$.We are given $E - A = 3$. Substituting $E = \frac{5}{4}A$,we get $\frac{5}{4}A - A = 3$,which simplifies to $\frac{1}{4}A = 3$,so $A = 12$.Using $A = 12$,we find $B = \frac{5}{6} 	imes 12 = 10$ and $E = 15$.We are given that the age of $F$ is less than $A$ $(12)$ but greater than $B$ $(10)$. Since all ages are integers,$F$ must be $11$.Therefore,the ratio of the ages of $A$ and $F$ is $12:11$.

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