Question

Present ages of john and paul are in the ratio of 5:4 respectively.three years hence the ration of tgeir ages will become 11:9.whats is pauls present age in years ?

Answer 1

Hey friend,

Here's the complete solution :-
Ratio of present ages of John and Paul = 5:4
Let the common multiple be 'x'.
Now, present age of John = (5x) years
Similarly, present age of Paul = (4x) years

Now,
After 3 years,
John's age = (5x + 3) years &
Paul's age = (4x + 3) years

The given ratio of their ages after three years = 11:9.

Therefore, we can say that,
(5x + 3)/(4x + 3) = 11/9
9(5x + 3) = 11(4x + 3)
45x + 27 = 44x + 33
45x - 44x = 33 - 27
x = 6

We have been asked Paul's present age i. e. 4x
Paul's age = 4x = (4)(6) = 24 years
Hence, Paul's present age is 24 years.

Answer 2

Answer:

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

$\rule{130}2$

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

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

$\rule{130}2$

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

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

$\rule{130}2$