Question

The ratio of present ages of Rehana and her mother is 2 : 7. After 2 years, the ratio of their ages will be 1 : 3. What is Rehana's present age?

Answer 1

Step 1: Represent present ages

Rehana’s age = 2x, Mother’s age = 7x

Step 2: After 2 years

After 2 years:

• Rehana's age will be 2x + 2
• Mother's age will be 7x + 2

The ratio of their ages after 2 years is given as 1 : 3. Hence:

`(2x+2)/(7x+2) = 1/3`

Step 3: Solve for x

3(2x + 2) = 1(7x + 2)

6x + 6 = 7x + 2

6x − 7x = 2 − 6

−x = −4

x = 4

Step 4: Find Rehana's present age

2x = 2(4) = 8 years.

Rehana's present age is: 8 years