Question

the ratio of present ages of p and q is 3:8 and after 6 years their ages ratio is 4:9 then the age of P at present is​

Answer 1

Answer:

18 years

Given,

Ratio of present ages of P and Q = 3 : 8

Ratio of ages of P and Q after 6 years = 4 : 9

To Find :-

Present age of P.

Solution :-

Ratio of present ages of P and Q = 3 : 8

According to this :-

Let,

Present age of P = 3x

Present age of Q = 8x

After 6 years their ages will be :-

P = 3x + 6

Q = 8x + 6

But they given they are in the Ratio :- 4 : 9

Equating both :-

$\sf\dfrac{3x + 6}{8x + 6} = \dfrac{4}{9}$

[Since, 4:9 can be written as $\dfrac{4}{9}$ also]

Cross Multiplying :-

9(3x + 6) = 4(8x + 6)

9(3x) + 9(6) = 4(8x) + 4(6)

27x + 54 = 32x + 24

Transposing constant terms to one side and Variable terms to other side :-

54 - 24 = 32x - 27x

30 = 5x

5x = 30

x = $\sf\dfrac{30}{5}$

x = 6

$\sf\therefore$ x = 6.

Present age of P = 3x = 3(6) = 18

$\sf\therefore$ Present age of P = 18years.

Answer 2

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