Average of five numbers is 61. If the average of first and third number is 69 and the average of second and fourth number is 69, what is the fifth number ?
- 31
- 29
- 25
- 35
The Correct Option is B
Solution and Explanation
Let the five numbers be a, b, c, d, e.
- Average of all five numbers = 61 → Sum of five numbers = 61 × 5 = 305.
- Average of 1st and 3rd = 69 → (a + c)/2 = 69 → a + c = 138.
- Average of 2nd and 4th = 69 → (b + d)/2 = 69 → b + d = 138.
Step 2 — Express total sum:
We know: a + b + c + d + e = 305.
Substitute values of (a + c) and (b + d):
→ (a + c) + (b + d) + e = 305.
→ 138 + 138 + e = 305.
Step 3 — Solve for e (fifth number):
276 + e = 305.
e = 305 − 276 = 29.
Step 4 — Conclude:
The fifth number is 29.
Answer: The correct option is (B) : 29.
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