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?

• A. 4 years
• B. 5 years
• C. 6 years
• D. 8 years

Hint:

Use ratio variables and average formulas to find unknowns. Be careful with the timeline when subtracting or adding years.

Answer 1

The Correct Option is B

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