Question

Five years ago A was thrice as old as B and 10 years later A shall be twice as old as B, what is the present age of A?​

Answer 1

$\large{\underline{\rm{\green{\bf{Given:-}}}}}$

Five years ago A was three times as old as B

Ten years later a shall be twice older than B

$\large{\underline{\rm{\green{\bf{To \: Find:-}}}}}$

Present age of A

Present age of B

$\large{\underline{\rm{\green{\bf{Solution:-}}}}}$

Let us consider the age of x to be a and B to be y

Given that, five years ago, a was thrice as old as b  

According to the question,

$\sf x-5=3(y-5)$

$\implies \sf x=y-10 \qquad ...(1)$

Then, after 10 years

$\sf x+10-2(y+10)$

$\implies \sf x=2y+10 \qquad ...(2)$

From the equation (1) and (2),

$\sf 3y-10=2y+10$

$\implies \sf y=20$

And therefore,

$\sf x=2y+10=2 \times 20+10= 50 \: years$

Age of x would be 50, and

y = 20 years

Hence age of A = 50 and B = 20