Question

20. 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.
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Answer 1

Given the ratio of present ages of Sonal and Manoj=7:5

Let the age of Sonal be 7x years and age of Manoj be 5x years

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

Given ratio of ages after 10 years=9:7

So now assume the ages be 9x and 7x

∴7x+10+5x+10=9x+7x

9x−5x=20

4x=20

x=5

So, the present age of Sonal=7x=7×5=35years

and the present age of Sonal=5x=5×5=25years

Answer 2

$\bf{\dag}\:{\underline{\underline{\sf{Question\::}}}}$

• 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.

$\bf{\dag}\:{\underline{\underline{\sf{Answer\::}}}}$

• Their present ages are 35 years and 25 years.

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━

$\bf{\dag}\:{\underline{\underline{\sf{Given\::}}}}$

• Ratio of ages of Sonal and Manoj = 7:5
• Ratio of their ages after ten years = 9:7

$\bf{\dag}\:{\underline{\underline{\sf{To\:Find\::}}}}$

• Their present ages?

$\bf{\dag}\:{\underline{\underline{\sf{Solution\::}}}}$

• Let present ages of Sonal and Manoj be 7y years and 5y years.
• Their ages after 10 years will be (7y + 10) and (5y + 10).

$\underline{\bm{\bigstar\:According\:to\:the\:Question\::}}$

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

Therefore,

$\\ :\implies\:\tt \dfrac{7y + 10}{5y + 10} = \dfrac{9}{7}$

By cross multiplication,

$\\ :\implies\:\tt 7(7y + 10) = 9(5y + 10)$

$\\ :\implies\:\tt 49y + 70 = 45y + 90$

$\\ :\implies\:\tt 49y - 45y = 90 - 70$

$\\ :\implies\:\tt 4y = 20$

$\\ :\implies\:\tt y = {\cancel{\dfrac{20}{4}}}$

$\\ :\implies\:{\large{\boxed{\tt{\red{y = 5}}}}}$

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━

So,

➬ Present age of Sonal = 7y

➬ Present age of Sonal = 7(5)

➬ Present age of Sonal = 7 × 5

➬ Present age of Sonal = 35 years

Also,

➬ Present age of Manoj = 5y

➬ Present age of Manoj = 5(5)

➬ Present age of Manoj = 5 × 5

➬ Present age of Manoj = 25 years

• Henceforth, their present ages are 35 years and 25 years.

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