Question

The ages of Sonal and Manoj are in the ratio 7:5. Ten years hence, the ratio of their ages
will be 9: 7. Find their present ages​

Answer 1

Answer:

let the age of Sonal be 7x years and the age of Manoj is 5x years

ten years later their age will be (7x+10) and (5x+10)

given ratio of their ages after 10 years=9:7

So,now assume the ages be 9x and 7x

7x+10+5x+10=9x+10x

9x-5x=20

4x=20

X=5

So, the present age of Sonal is 7x=7x5=35years

the present age of Manoj is 5x=5x5=25years

Answer 2

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Sonal and Manoj age are in the ratio = 7 : 5
• After 10 years the ratio will be = 9 : 7

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• Original age = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

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let the original age be 7x and 5x

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after 10 years age will be 7x + 10 and 5x + 10

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ATQ:-

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$\sf: \implies\: {\bold{ \dfrac{7x+10}{5x + 10}= \dfrac{9}{7}}}$

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$\sf: \implies\: {\bold{ 7 ( 7x + 10) = 9 ( 5x + 10 )}}$

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$\sf: \implies\: {\bold{ 49x + 70 = 45x + 90 }}$

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$\sf: \implies\: {\bold{ 49x - 45x = 90 - 70}}$

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$\sf: \implies\: {\bold{ 4x = 20}}$

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$\sf: \implies\: {\bold{ x = \dfrac{20}{4}}}$

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$\sf: \implies\: {\bold{ x = 5 }}$

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• Finding the number

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7x = 7 × 5 = 35 years

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5x = 5 × 5 = 25 years

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Original age of Sonal and Manoj is 35 years and 25 years