Question
The average of 11 numbers is 50. The average of the
first six numbers is 48 and the average of the last six numbers is 52. Find the 6th number.Solution
Total sum of 11 numbers = 11 × 50 = 550 Sum of first 6 numbers = 6 × 48 = 288 Sum of last 6 numbers = 6 × 52 = 312 The 6th number is counted in both these sums. So: (First 6 sum) + (Last 6 sum) − (6th number) = Total sum 288 + 312 − x = 550 600 − x = 550 ⇒ x = 50 6th number = 50.
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