Question

Two years ago, Montu was three times as old as his daughter and two years hence, twice his age will be equal to five times that of his daughter. Find their present ages.

Answer 1

Let the present age of Montu be $x$ years and his daughter be $y$ years

According to question

$\Rightarrow$ $(x-2)=3(y-1)\Rightarrow x(x+2)=5(y+2)$

$\Rightarrow$ $x-2=3y-6$ $\Rightarrow 2x+4=5y+10$

$\Rightarrow x-3y=-\mathrm{4....}\left(1\right)$ $\Rightarrow$ $2x-5y=\mathrm{6.....}\left(2\right)$

Solving equation (1) and (2) by elimination method

$x-3y=-\mathrm{4.....}\left(1\right)\times 2$

$2x-5y=\mathrm{6.....}\left(2\right)\times 1$

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$2x-6y=-8$

$2x-5y=6$

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$-y=-14$

$y=14$

$x=-4+3y=-4+3\times 14=-4+42=38$

present age of montu $=38$ years

present age of his daughter $=14$ years