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The average age of eight boys increases by three months, if a 16-year old boy is replaced by a new boy. The age of the new boy is:
17 years
17 years 2 months
17 years 6 months
18 years
18 years
Multiply the total count by the increase in age and add it to the age of the replaced person. Here, 8├Ч3┬аmonths=24┬аmonths, which is 2┬аyears. Adding this to 16┬аyears gives 18┬аyears.
Number of boys = 8, Age of replaced boy = 16 years, Average age increase = 3 months.
Age┬аof┬аnew┬аboy=Age┬аof┬аreplaced┬аboy+(Number┬аof┬аboys├ЧIncrease┬аin┬аaverage)
Multiply the total count by the increase in age and add it to the age of the replaced person. Here, 8├Ч3┬аmonths=24┬аmonths, which is 2┬аyears. Adding this to 16┬аyears gives 18┬аyears.
Many students convert the increase of 3 months into years incorrectly or forget to multiply the increment by the total count of members.
Identify given values
Total number of boys is n=8. The age of the boy replaced is 16┬аyears. The average increase is 3┬аmonths, which is equal to 123тАЛ=0.25┬аyears.
n=8,┬аAge┬аof┬аreplaced┬аboy=16,┬аIncrease=123тАЛ┬аyears
Apply calculation formula
The total increase in the sum of ages is the product of the number of boys and the increase per boy. Calculation: 8├Ч3┬аmonths=24┬аmonths.
Total┬аIncrease=8├Ч3┬аmonths=24┬аmonths=2┬аyears
Calculate the new boy's age
The age of the new boy is the sum of the replaced boy's age and the total increase in age.
New┬аAge=16┬аyears+2┬аyears=18┬аyears
D is correct because the new boy's age is calculated as the sum of the replaced boy's age and the total net gain of 24┬аmonths, resulting in 18┬аyears.
This concept of 'replacement in an average' is frequently tested in mixtures and alligation problems as well as time-speed-distance average speed calculations.