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Sia ? 6 years, 4 months ago
Let the present ages of B and A be x years and y years respectively.
Then,
B's age 5 years ago = {tex}(x - 5) years{/tex}
and A's age 5 years ago = {tex}(y - 5) years.{/tex}
{tex}\therefore{/tex} {tex}(y - 5) = 3(x - 5){/tex} {tex}\Rightarrow{/tex}{tex}3x -y = 10{/tex} .... (i)
B's age 10 years hence = {tex}(x +10) years{/tex}.
A's age 10 years hence = {tex}(y +10) years{/tex}.
{tex}\therefore{/tex} {tex}(y + 10) = 2(x + 10){/tex} {tex}\Rightarrow{/tex} {tex}2x - y = - 10{/tex} ..... (ii)
On subtracting (ii) from (i), we get x = 20.
Putting x = 20 in (i), we get
(3{tex}\times{/tex}20) - y = 10 {tex}\Rightarrow{/tex}y = 60 -10 = 50.
{tex}\therefore{/tex} x = 20 and y = 50.
{tex}\text{Hence, B's present age = 20 years}{/tex}
{tex}\text{and A's present age = 50 years.}{/tex}
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