Question : The average of twenty-five numbers is 54. The average of the first 13 numbers and that of the last 13 numbers is 52.8 and 62.2, respectively. If the 13th number is excluded, then what is the average of the remaining numbers (corrected to one decimal place)?
Option 1: 50.6
Option 2: 49.8
Option 3: 51.2
Option 4: 50.2
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Correct Answer: 50.2
Solution :
Sum of the 25 numbers = 54 × 25 = 1350
Sum of the first 13 numbers = 13 × 52.8 = 686.4
Sum of the last 13 numbers = 13 × 62.2 = 808.6
13
th
number = (Sum of the first 13 numbers + Sum of the last 13 numbers) – (Sum of the 25 numbers)
⇒ 13
th
number = (686.4 + 808.6) – (1350) = 1495 – 1350 = 145
Sum of the remaining 24 numbers = (1350 – 145) = 1205
$\therefore$ Average of the remaining 24 numbers $=\frac{1205}{24} = 50.2$
Hence, the correct answer is 50.2.
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