The average age of 3 students is 21 years. The ratio of their ages is x : y : z where x : y = 1 : 2 and y : z = 1 : 3. Find the v…

Question

The average age of 3 students is 21 years. The ratio of their ages is x : y : z where x : y = 1 : 2 and y : z = 1 : 3. Find the value of y.

1. A. 13
2. B. 14 (Correct answer)
3. C. 21
4. D. 7

Correct Answer

Option B — 14

Detailed Solution & Explanation

The correct answer is 14.

Key Points

• First combine the two partial ratios into a single continued ratio, then use the average.
• Given x : y = 1 : 2 and y : z = 1 : 3.
• To join them, make the common term y equal. In the first ratio y = 2, in the second y = 1; scale the second by 2 → y : z = 2 : 6.
• So the combined ratio is x : y : z = 1 : 2 : 6.
• The average age of 3 students is 21, so their total age = 3 × 21 = 63.
• Total ratio parts = 1 + 2 + 6 = 9, hence 1 part = 63 ÷ 9 = 7.
• Therefore y = 2 parts = 2 × 7 = 14 years.
• to chain ratios a : b and b : c, scale them so the shared term matches, giving a : b : c in one line.

Exam Tip

• average × number of items = total; splitting the total by ratio parts is the fastest route to any single share.