The average of n numbers is 55. If 70% of the numbers are decreased by 3 each and the remaining numbers are increased by 5 each, then what is the average of the resulting numbers?
- A54.1
- B53.5
- C54.4
- D53.8
Solution & Step-by-step Explanation
Let the total number of elements be 100.
70% of the numbers = 70
Remaining 30% of the numbers = 30
The net change in the total sum is given by:
Net Change=70×(−3)+30×(+5)
Net Change=−210+150=−60
The change in the average is:
Change in Average=
Total Numbers
Net Change
=
100
−60
=−0.6
Therefore, the new average is:
New Average=Old Average+Change in Average=55−0.6=54.4
70% of the numbers = 70
Remaining 30% of the numbers = 30
The net change in the total sum is given by:
Net Change=70×(−3)+30×(+5)
Net Change=−210+150=−60
The change in the average is:
Change in Average=
Total Numbers
Net Change
=
100
−60
=−0.6
Therefore, the new average is:
New Average=Old Average+Change in Average=55−0.6=54.4