Question

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

Answer 1

Given:

• Ratio of ages of Sonal and Manoj is 7:5.
• Ten years hence , the ratio of their ages will be 9:7.

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To find:

• Present age of Sonal and Manoj?

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Solution:

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☯ Let present age of Sonal and Manoj be 7x and 5x respectively.

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$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

• Ten years hence , the ratio of their ages will be 9:7.

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Their ages after 10 years,

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• Age of Sonal = (7x + 10) years
• Age of Manoj = (5x + 10) years

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Therefore,

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

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

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

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

$:\implies\sf 4x = 20$

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

$:\implies{\underline{\boxed{\sf{\purple{x = 5}}}}}\;\bigstar$

Hence,

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• Present age of Sonal, 7x = 7 × 5 = 35 years.
• Present age of Manoj, 5x = 5 × 5 = 25 years.

Answer 2

Answer:

Given :-

• The age of Sonal and Manoj are in the ratio of 7:5 .
• Ten years ago, their ratio of their ages will be 9:7 .

To Find :-

• What is their present ages .

Solution :-

» Let, the present age of Sonal be 7x

And, the present age of Manoj will be 5x

➟ After 10 years,

» Age of Sonal will be (7x + 10)

» And, age of Manoj will be (5x + 10)

➣ According to the question,

⇒ $\dfrac{(7x + 10)}{(5x + 10}$ = $\dfrac{9}{7}$

⇒ 7(7x + 10) = 9(5x + 10)

⇒ 49x + 70 = 45x + 90

⇒ 49x - 45x = 90 - 70

⇒ 4x = 20

⇒ x = $\sf\dfrac{\cancel{20}}{\cancel{4}}$

➠ x = 5 years

Hence, their required present ages will be,

◪ Present age of Sonal = 7x = 7(5) = 35 years.

◪ Present age of Manoj = 5x = 5(5) = 25 years.

$\therefore$ The present age of Sonal is 35 years and the present age of Manoj will be 25 years .