Question

the ages of sonal and manoj are in the ratio 7:5 . Twn years hence the ratio of their ges will be 9 : 7. Find their present age.

Answer 1

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Answer 2

Note: There is a spelling error in the question as 'twn' may be taken as 'ten' as well as 'two'. I have given here solutions for both the time-frames.

Solution: Taking time as "after ten years"

Let the ages be (Sonal) 7x and (Manoj) 5x

After 10 years

Sonal = (7x + 10)

Manoj = ( 5x + 10 )

Ratio of ages after 10 years = 9 : 7

ACQ

$\frac{7x + 10 }{5x + 10} = \frac{9}{7} \\\\ by \ cross \ multiplying \ \\\\ 49x + 70 = 45x + 90 \\\\ 49x - 45x = 90 - 70 \\\\ 4x = 20 \\\\ x = \frac{20}{4} \\\\ x = 5$

Present ages are -

$Sonal : 7x = 7 \times 5 = 35 \ years \\ Manoj : 5x = 5 \times 5 = 25 \ years$

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Solution: Taking time as  "after two years" 

Let Present ages:  Sonal = 7x and Manoj = 5x

After two years

Sonal = 7x +2

Manoj = 5x +2

Ratio after two years = 9 : 7

ACQ 

(7x +2) / (5x +2) = 9/7

⇒ 49x + 14 = 45x + 18

⇒ 49x - 45x = 18 - 14

⇒ 4x = 4 

⇒ x=1

∴  The present ages 

Sonal = 7x = 7 years

Manoj = 5x = 5 years.

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