The arithmetic mean of 25 real numbers is 110. If 10 numbers are increased by $$121212\frac{1}{2}1221$$ 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:

Given:Mean of 25 numbers = 110 Original total = 25×110=2750. \\times 110 = 2750.×110=2750.10 numbers increased by 1212=12.$$2\\frac{1}{2}$$ = 12.221=12.5 each.Another 10 numbers increased by 15 each.Remaining 5 numbers unchanged.Formula Used:New mean =New totalNumber of items= \\dfrac{$$\\text{New total}$$}{$$\\text{Number of items}$$}=Number of itemsNew totalSolution:Total increment =10×12.5+10×15=125+150=275 10 \\times 12.5 + 10 \\times 15 = 125 + 150 = 27510×12.5+10×15=125+150=275New total = 2750 + 275 = 3025.New mean =302525=12 $$\\dfrac{3025}{25}$$ = 12253025=121.

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The arithmetic mean of 25 real numbers is 110. If 10 numbers are increased by 121212\frac{1}{2}1221 each, another 10 numbers are increased

Question

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:

125

121

120

112

Solution

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.