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 age.

Answer 1

Given

• Present age of ram and rehman in ratio 8:9

• After 5 years age of ram and rehman will be 9:10.

What To Find

• Present age of Ram and Rehman.

Solution

Let assume present age of ram and rehman be x

Present age

• Age of rehman is 8x
• Age of rehman is 9x

After 5 years their ages will be

• Age of ram is (8x + 5)

• Age of rehman is (9x + 5)

According to the question

$\begin{cases} \\ \large\bf{\red{ \implies}} \tt \: \frac{8x + 5}{9x + 5} \: = \: \frac{9}{10} \\ \\\bf{\blue{ \implies}} \rm\: Now , We \: will \: do \: cross - multiply \\ \\\large\bf{\red{ \implies}} \tt \: 10(8x + 5) \: = \: 9(9x + 5) \\ \\\large\bf{\red{ \implies}} \tt \: 80x \: + \: 50 \: = \: 81x \: + \: 45 \\ \\ \large\bf{\red{ \implies}} \tt \: 81x \: - \: 80x\: = \: 50 \: - \: 45 \\ \\\large\bf{\red{ \implies}} \tt \: x \: = \: 5 \\ \end{cases}$

We know,

• Age of ram is 8x
• Age of rehman is 9x

Putting the values of x

☛ Present age of ram

⇛8x = 8 × 5 = 40

☛ Present age of rehman

⇛9x = 9 × 5 = 45

• Present age of ram is 40 year's

• Present age of rehman is 45 year's