Question

ages of roopa and her sister is in ratio 3 : 2 after 5 years the ratio becomes 4 :
3 find their present ages ​

Answer 1

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Answer 2

Answer:

Roopa is 15 years old and her sister is 10 years old.

Step-by-step explanation:

Given :

Ratio of present ages of Roopa and her sister = 3 : 4

Ratio of ages after 5 years = 4 : 3

To find :

Their present ages

Solution :

Let the present ages be -

• Roopa as 3x
• Her sister as 2x

★ $\green{\boxed{\green{\boxed{\red{\sf{\frac{3x + 5}{2x + 5} = \frac{4}{3}}}}}}}$

$\sf{\implies} \: \dfrac{3x + 5}{2x + 5} = \dfrac{4}{3} \\ \sf{\implies} \: 3(3x + 5) = 4(2x + 5) \\ \sf{\implies} \: 9x + 15 = 8x + 20 \\ \sf{\implies} \: 9x - 8x = 20 - 15 \\ \sf{\implies} \: x = 5$

★ Value of 3x

$\sf{\implies} \: 3(5) \\ \sf{\implies} \: 15$

Roopa's present age = 15 years

$\rule{300}{1.5}$

★ Value of 2x

$\sf{\implies} \: 2(5) \\ \sf{\implies} \: 10$

Her sister's present age = 10 years

$\therefore$ Roopa is 15 years old and her sister is 10 years old.