Question

The ages of A and B are in the ratio 8:3. Six years hence, there ages will be in the ratio 9:4 . Find their present ages​

Answer 1

Given

• Present age of A and B in ratio 8:3

• After 6 years ages of A and B will be 9:4

What To Find

• Present age of A and B

Solution

Let assume the present age of A and B is x

Present age

• Age of A is 8x
• Age of B is 3x

After 6 years their ages will be

• Age of A is (8x + 6)

• Age of B is (3x + 6)

According to the question

$\begin{cases} \\ \large\bf{\orange{ \implies}} \tt \: \frac{8x + 6}{3x + 6} \: = \: \frac{9}{4} \\ \\ \bf{\pink{ \implies}} \rm \: Now , We \: will \: do \: cross - multiply \\ \\ \large\bf{\orange{ \implies}} \tt \: 4(8x + 6) \: = \:9(3x + 6) \\ \\ \large\bf{\orange{ \implies}} \tt \: 32x \: + \: 24 \: = \: 27x \: + \: 54 \\ \\ \large\bf{\orange{ \implies}} \tt \: 32x \: - \: 27x \: = \: 54 \: - \: 24 \\ \\ \large\bf{\orange{ \implies}} \tt \: 5x \: = \:30 \\ \\ \large\bf{\orange{ \implies}} \tt \: x \: = \: \frac{ \cancel{30} \: \: ^{6} }{ \cancel{5}} \\ \\ \large\bf{\orange{ \implies}} \tt \: x \: = \: 6 \\ \end{cases}$

We know ,

• Age of A is 8x
• Age of B is 3x

Putting the values of x

☛ Present age of A

⇛ 8x = 8 × 6 = 48

☛ Present age of B

⇛ 3x = 3 × 6 = 18

• Present age of A is 48 year's

• Present age of B is 18 year's