Question : The average of n numbers is 42. If 75% of the numbers are increased by 4 each and the remaining numbers are decreased by 8 each, then what is the average of the numbers, so obtained?
Option 1: 44
Option 2: 42.5
Option 3: 43
Option 4: 43.8
Correct Answer: 43
Solution :
The average of n numbers is 42, so the total sum of these numbers is 42n.
If 75% of the numbers are increased by 4 each.
The total increase in the sum of these numbers = 0.75n × 4 = 3n
The remaining 25% of the numbers are decreased by 8 each.
The total decrease in the sum of these numbers = 0.25n × 8 = 2n
The new sum of the numbers = 42n + 3n – 2n = 43n
Since the number of elements 'n' hasn't changed, the new average = $\frac{43n }{ n}$ = 43
Hence, the correct answer is 43.
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