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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?
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Solution
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
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