The ratio of the present ages of A and B is 8 : 9. After 9 years, this will become 19 : 21. C is 3 years younger to B. What is the present age (in years) of C?Options4948515
Question
The ratio of the present ages of A and B is 8 : 9. After 9 years, this will become 19 : 21. C is 3 years younger to B. What is the present age (in years) of C?Options4948515
Solution
Let's solve this step by step:
Step 1: Let's assume the present ages of A and B are 8x and 9x years respectively.
Step 2: According to the problem, after 9 years, the ratio of A's and B's ages will be 19:21. So, we can write it as (8x+9) / (9x+9) = 19/21.
Step 3: Cross-multiplying gives us 21*(8x+9) = 19*(9x+9).
Step 4: Simplifying this, we get 168x + 189 = 171x + 171.
Step 5: Rearranging the terms, we get 171x - 168x = 189 - 171.
Step 6: This simplifies to 3x = 18, so x = 18/3 = 6.
Step 7: Substituting x = 6 in 9x (B's present age), we get B's present age = 9*6 = 54 years.
Step 8: Since C is 3 years younger than B, C's present age = 54 - 3 = 51 years.
So, the present age of C is 51 years.
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