Question:
The ratio of present ages of A, B, and C is 3 : 4 : 5. After 6 years, the average age of all the three will be 26 years. What was the difference between the ages of B and C, 4 years ago?
The ratio of present ages of A, B, and C is 3 : 4 : 5. After 6 years, the average age of all the three will be 26 years. What was the difference between the ages of B and C, 4 years ago?
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Use ratio variables and average formulas to find unknowns. Be careful with the timeline when subtracting or adding years.
Updated On: Apr 21, 2025
- 4 years
- 5 years
- 6 years
- 8 years
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The Correct Option is B
Solution and Explanation
Let present ages be:
- A = 3x
- B = 4x
- C = 5x
After 6 years, their ages will be:
- A = 3x + 6
- B = 4x + 6
- C = 5x + 6
Average age after 6 years:
\[
\frac{(3x + 6) + (4x + 6) + (5x + 6)}{3} = 26
\Rightarrow \frac{12x + 18}{3} = 26
\Rightarrow 12x + 18 = 78 \Rightarrow 12x = 60 \Rightarrow x = 5
\]
So present ages:
- A = 15, B = 20, C = 25
4 years ago:
- B = 16, C = 21
Difference = \( 21 - 16 = 5 \) years
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