Question

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Answer 1

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 ages.

Statement:

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.

Solution:

• Let the present age of Ram and Rehman be 8x years and 9x years respectively.
• After 5 years, their ages will be 9x years and 10 years respectively.
• Therefore, by the problem

$\frac{8x + 5}{9x + 5} = \frac{9}{10} \\ = > 10(8x + 5) = 9(9x + 5) \\ = > 80x + 50 = 81x + 45 \\ = > 50 - 45 = 81x - 80x \\ = > x = 5$

• So, the present age of Ram = 8x years = (8×5) years = 40 years
• The present age of Rehman = 9x years = (9×5) years = 45 years

Answer:

The present ages of Ram and Rehman are 40 years and 45 years respectively.