The present ages of A and B are in the ratio 3 : 4. Ten years ago, this ratio was 4 : 7. The present ages of A and B are respectively?
Question
The present ages of A and B are in the ratio 3 : 4. Ten years ago, this ratio was 4 : 7. The present ages of A and B are respectively?
Solution
Let's solve this step by step:
Step 1: Let's assume the present ages of A and B are 3x and 4x respectively.
Step 2: According to the problem, ten years ago, the ratio of their ages was 4 : 7. So, we can write it as (3x - 10) / (4x - 10) = 4/7.
Step 3: Cross-multiplying gives us 7*(3x - 10) = 4*(4x - 10).
Step 4: Simplifying this, we get 21x - 70 = 16x - 40.
Step 5: Rearranging the terms, we get 21x - 16x = 70 + 40.
Step 6: Simplifying further, we get 5x = 110.
Step 7: Solving for x, we get x = 22.
Step 8: Substituting x = 22 in 3x and 4x, we get the present ages of A and B as 66 and 88 respectively.
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