The ratio of present ages of Rahul and his sister is 3 : 4. Before 10 years the ratio of their ages was 13 : 19. What is Rahul's present age (in years)?
Question
The ratio of present ages of Rahul and his sister is 3 : 4. Before 10 years the ratio of their ages was 13 : 19. What is Rahul's present age (in years)?
Solution
Let's solve this step by step:
Step 1: Let's assume the present age of Rahul as 3x and the present age of his sister as 4x.
Step 2: According to the problem, 10 years ago, the ratio of their ages was 13:19. So, we can write this as (3x-10)/ (4x-10) = 13/19.
Step 3: Cross-multiplying the equation, we get 19*(3x-10) = 13*(4x-10).
Step 4: Simplifying the equation, we get 57x - 190 = 52x - 130.
Step 5: Rearranging the terms, we get 57x - 52x = 190 + 130.
Step 6: Simplifying further, we get 5x = 320.
Step 7: Solving for x, we get x = 320/5 = 64.
Step 8: Substituting x = 64 in 3x, we get Rahul's present age as 3*64 = 192 years.
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