Question

The ages of Rakesh and Roshan are in the ratio 4:5. Four years from now, the ratio of their ages will be 9:11. Find their present ages.

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Answer 1

❐ EXPLANATION:

.

$\text {Let's,}$

• $\text {The age of Rakesh be 4x.}$

$\text {So,}$

• $\text {The age of Roshan should be 5x.}$

$\underline \text {After 4 years,}$

• $\text {The age of Rakesh should be 4x + 4.}$

$\text {And,}$

• $\text {The age of Roshan should be 5x + 4.}$

$\underline \text {According To Question,}$

$\hookrightarrow (4x + 4) : (5x + 4) = 9 : 11$

$\hookrightarrow \frac{4x + 4}{5x + 4} = \frac{9}{11}$

$\hookrightarrow 11 (4x + 4) = 9 (5x + 4)$

$\hookrightarrow 44x + 44 = 45x + 36$

$\hookrightarrow 44 - 36 = 45x - 44x$

$\hookrightarrow \red{ \boxed{x = 8} }$

$\text {The age of Rakesh is 32 years (4(8) = 32).}$

$\text {The age of Roshan should is 40 years (5(8) = 40).}$

❐ FINAL ANSWER:

.

• The Age of Rakesh and Roshan are 32 and 40 years respectively.

Answer 2

Answer:

Let their present age be 4a and 5a.

After 8 years, their ages will be (4a+8) and (5a+8)

Ratio would be (4a+8) : (5a+8)

But this ratio is given to be 5:6. Therefore

(4a+8) : (5a+8) = 5:6

solve this (4a+8) / (5a+8) = 5/6

=> 6 x (4a+8) = (5a+8) x 5

=> 24a + 48 = 25a + 40

=> a = 8

So their present age would be

4a = 4x8 = 32

5a = 5x8 = 40

Step-by-step explanation:

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