Question

The present ages of Ram and Rehman are in the ratio 8:9. After 5 years, the ratio of their ages will be 9:10
Find their present ages.
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Answer 1

Step-by-step explanation:

Let the present ages of Ram and Rehman be 8x and 9x.

After 5 years, the ratio of their ages will be 9:10.

begin mathsize 16px style fraction numerator 8 straight x space space plus space 5 over denominator 9 straight x space plus space 5 end fraction space equals space 9 over 10 end style

→ 10(8x + 5) = 9(9x + 5)

→ 80x + 50 = 81x + 45

→ x = 5

Present age of Ram = 8x = 8 × 5 = 40 years

Present age of Rehman = 9x = 9 × 5 = 45 years

Answer 2

✦ Given ;

• Present ages of Ram and Rehman are in the ratio 8 : 9. 5 years from now, the ratio of their ages will be 9 : 10.

✦ To Find

• What's their present ages ?

✦ Solution

Consider Ram present age = 8x years

Rehman present age = 9x years

Five years later, Anu age = ( 8x + 5 ) years

Rehman age = ( 9x + 5 ) years

As per the Question ,

$\sf{\dfrac{8x + 5}{9x + 5} = \dfrac{9}{10}}$

By cross multiplication, we have

$:\implies \sf{10 ( 8x + 5 ) = 9 ( 9x + 5 )}$

$:\implies \sf{80x + 50 = 81x + 45 }$

$:\implies \sf{50 - 45 = 81x - 80x }$

$\boxed{\therefore \sf{5 = x}}$

Hence ,

Ram present age = 8x years = ( 8 × 5 ) years = 40 years.

Rehman present age = 5x years = ( 9 × 5 ) years = 45 years.