The ages of A and B are presently in the ratio of 3 : 5. Nine years ago this ratio will become 12 : 23. What is the present age of A?
Question
The ages of A and B are presently in the ratio of 3 : 5. Nine years ago this ratio will become 12 : 23. What is the present age of A?
Solution
Let's solve this step by step:
Step 1: Let's assume the present ages of A and B are 3x and 5x respectively.
Step 2: According to the problem, nine years ago, the ratio of their ages was 12:23. So, we can write this as (3x - 9) / (5x - 9) = 12/23.
Step 3: Cross-multiplying gives us 23*(3x - 9) = 12*(5x - 9).
Step 4: Simplifying this, we get 69x - 207 = 60x - 108.
Step 5: Rearranging the terms, we get 69x - 60x = 207 + 108.
Step 6: This simplifies to 9x = 315.
Step 7: Solving for x, we get x = 315 / 9 = 35.
Step 8: Substituting x = 35 in 3x gives us the present age of A, which is 3*35 = 105 years.
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