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.
Similar Questions
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?
Eighteen years ago, the ratio of A’s age to B’s age was 8 : 13. Their present ratios are 5 : 7. What is the present age of A
Present age ratio of A and B is 2 : 3. After 12 years their age ratio will be 3 : 4. Find the present age of A.
10 years ago, the ratio of ages of A and B was in the ratio 7:10. 6 years hence, their ages will be in the ratio 5:6. What is the difference of their ages?
The ages of A, B, and C are in the ratio 3:5:7. If the sum of their ages is 90 years, how old is B? Options 20 30 25 35
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.