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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