Question

present age of Reema and Shalini are in the ratio 5:8 4 years from now the ratio of their age will be 2:3 find the present age​

Answer 1

Answer:

The present ages of Reema and Shalini are 20 years and 32 years respectively.

Step-by-step explanation:

Given :

Reema and Shalini's present age ratio = 5 : 8

Ratio of ages after 4 years = 2 : 3

To find :

Their present ages

Solution :

Let the present ages be -

• Reema as 5x
• Shalini as 8x

$\rule{300}{1.5}$

After 4 years -

• Reema = (5x + 4)
• Shalini = (8x + 4)

$\rule{300}{1.5}$

★ $\boxed{\bf{\frac{(5x + 4)}{(8x + 4)} = \frac{2}{3}}}$

$\sf{\implies} \: \frac{(5x + 4)}{(8x + 4)} = \frac{2}{3} \\ \sf{\implies} \:cross \: multiply \\ \sf{\implies} \:3(5x + 4) = 2(8x + 4) \\ \sf{\implies} \:15x + 12 = 16x + 8 \\ \sf{\implies} \:15x - 16x = 8 - 12 \\ \sf{\implies} \:\cancel - x = \cancel - 4 \\ \implies\small{\green{\boxed{\green{\boxed{\red{\textsf{x = 4}}}}}}}$

$\rule{300}{1.5}$

★ Value of 5x

$\sf{\implies} \:5(4) \\ \sf{\implies} \:20$

Reema's present age = 20 years

$\rule{300}{1.5}$

★ Value of 8x

$\sf{\implies} \:8(4) \\ \sf{\implies} \:32$

Shalini's present age = 32 years

$\therefore$ The present ages of Reema and Shalini are 20 years and 32 years respectively.

Answer 2

Answer :-

20 years and 32 years are the present ages of Reema and Shalini respectively.

Explanation :-

Ratio of the present ages of Reema and Shalini = 5 : 8

Let the present age of Reema be '5x' years and let the present age of Shalini be '8x' years

Age of Reema after 4 years = (5x + 4) years

Age of Shalini after 4 years = (8x + 4) years

Given

Ratio of the ages Reema and Shalini after 4 years = 2 : 3

⇒ (5x + 4)/(8x + 4) = 2/3

By cross multiplication

⇒ 3(5x + 4) = 2(8x + 4)

⇒ 15x + 12 = 16x + 8

⇒ 12 - 8 = 16x - 15x

⇒ 4 = x

⇒ x = 4

Present age of Reema = 5x = 5(4) = 20 years

Present age of Shalini = 8x = 8(4) = 32 years

Therefore 20 years and 32 years are the present ages of Reema and Shalini respectively.