Question

Present ages of john and paul are in the ratio of 5 : 4 respectively. three years hence, the ratio of their ages will become 11 : 9 respectively. what is paul's present age in years?

Answer 1

Let x and y be the present ages of John and Paul

So,

x/y = 5/4.................1)

According to the second condition,

(x+3)/(y+3) = 11/9

9x + 27 = 11y + 33

9x - 11y = 6.................2)

From 1) and 2)

9 × (5/4) y - 11y = 6

45y/4 - 11y = 6

(45y -44y)/4 =6

y=24

Substituting y=24 in equation 1)

x = (5×24)/4

x = 30

So,

The present ages of John and Paul are 30 and 24 years respectively

Hope this helps !!!!!!!!

Answer 2

Answer:

Let the present age of John be 5x and Paul be 4x respectively.

$\rule{130}2$

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies\sf \dfrac{John+3}{Paul+3}=\dfrac{11}{9}\\\\\\:\implies\sf \dfrac{5x + 3}{4x + 3} = \dfrac{11}{9} \\\\\\:\implies\sf (5x + 3) \times 9= 11 \times (4x + 3)\\\\\\:\implies\sf 45x + 27 = 44x + 33\\\\\\:\implies\sf 45x - 44x = 33 - 27\\\\\\:\implies\:\underline{\boxed{\red{\bf x = 6\:years}}}\: \orange\bigstar$

$\rule{130}2$

☯ $\underline{\boldsymbol{Present\: Age\:of\: John\:\&\: Paul:}}$

$\bullet\:\:\textsf{John = 5x = 5(6) = \textbf{30 years}}\\\bullet\:\:\textsf{Paul = 4x = 4(6) = \textbf{24 years}}$

$\rule{130}2$