Question : The average of n numbers is 45. If 60% of the numbers are increased by 5 each and the remaining numbers are decreased by 10 each, then what is the average of the numbers so obtained?
Option 1: 42
Option 2: 43
Option 3: 46
Option 4: 44
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Correct Answer: 44
Solution :
Let the n = $10x$
60% of n = $6x$
Each of the $6x$ numbers increased by 5.
So, Net increase = $+30x$
40% of n = $4x$
Each of the $4x$ numbers decreased by 10.
So, Net decrease = $-40x$
Net increment or decrement in sum of numbers = $-40x + 30x = -10x$
Net increment or decrement in average = $-10x \div 10x = -1$
New average = $45 -1$ = $44$
Hence, the correct answer is 44.
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