The average of 11 numbers is 68. If the average of the first five is 63 and the average of the last five is 72, find the 6th numb…

Question

The average of 11 numbers is 68. If the average of the first five is 63 and the average of the last five is 72, find the 6th number.

1. A. 73 (Correct answer)
2. B. 74
3. C. 75
4. D. 76

Correct Answer

Option A — 73

Detailed Solution & Explanation

The correct answer is 73.

Key Points

• Convert every average into a total, since totals can be added and subtracted:
  • All 11 numbers: 11 × 68 = 748
  • First five: 5 × 63 = 315
  • Last five: 5 × 72 = 360
• The first five and last five together account for ten numbers, leaving only the 6th:
  • 6th number = 748 − 315 − 360 = 73
• The 6th number belongs to neither group, so nothing is double-counted here. Where a question makes the overlapping term part of *both* groups, you must add it back — check which case you are in before subtracting.

Additional Information

• Convert averages to totals before combining them; totals add and subtract cleanly, averages do not.
• Where two overlapping groups are given, the shared term is counted twice, so it must be added back: overlap = (sum of both groups) − (total of all).
• Here the two groups of five are disjoint and together cover ten of the eleven numbers, so straightforward subtraction isolates the missing term.

प्रश्न (हिन्दी में)

11 संख्याओं का औसत 68 है। यदि प्रथम पाँच का औसत 63 है और अंतिम पाँच का औसत 72 है, तो छठी संख्या ज्ञात कीजिए।

1. A. 73
2. B. 74
3. C. 75
4. D. 76