Question

The ratio of the present age of X and Y is 11:20 respectively. Seven years ago, X was 5/11 of Y in age. Find the difference between their present ages.​

Answer 1

Explanation:

Given, ratio of ages of X and Y is 11 : 20, meaning their ages can also be denoted by fraction 11/20.

Let their present ages be 11x and 20x.

Seven years ago, their ages will be 11x - 7 and 20x - 7 respectively.

But, it is given that X was 5/11 of Y.

Thus,

$\mathsf{11x-7=\frac{5}{11}(20x-7)}$

$\mathsf{==>11(11x-7)=5(20x-7)}$

$\mathsf{==>121x-77=100x-35}$

$\mathsf{==>121x-100x=-35+77}$

$\mathsf{==>21x=42}$

∴ $\mathsf{x=\frac{42}{21}=2}$

∴ $\mathsf{Present\:age\:of\:X=11\times2=22\:years}$

$\mathsf{Present\:age\:of\:Y=20\times2=40\:years}$

∴ $\mathsf{Difference\:between\:their\:ages=40-22=18\:years}$

Answer: 18 years

I hope this helps. :D