The arithmetic mean of 25 real numbers is 110. If 10 numbers are increased by $$12\frac{1}{2}$$ each, another 10 numbers are increased by 15 each and the remaining 5 numbers are unaltered, then the new value of the arithmetic mean is:​

Correct option is B

Given:

Mean of 25 numbers = 110

Original total = 25$$\times 110 = 2750.$$​​

10 numbers increased by 1$$2\frac{1}{2} = 12.$$​5 each.

Another 10 numbers increased by 15 each.

Remaining 5 numbers unchanged.

Formula Used:

New mean $$= \dfrac{\text{New total}}{\text{Number of items}}$$​​

Solution:
Total increment =$$10 \times 12.5 + 10 \times 15 = 125 + 150 = 275$$​​
New total = 2750 + 275 = 3025.
New mean =$$\dfrac{3025}{25} = 12$$​1.