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The average age of six girls increases by four months, if a 12 - year old girl is replaced by a new girl. The age of the new girl is:
16 years
15 years
14 years
13 years
14 years
Since the average increases by 4 months for 6 girls, the total increase is 6├Ч4=24 months. Convert 24 months to years (2 years) and add it to the replaced girl's age: 12+2=14 years.
Number of girls = 6, age of replaced girl = 12 years, increase in average age = 4 months.
AgenewтАЛ=AgereplacedтАЛ+(n├Ч╬ФA)
Since the average increases by 4 months for 6 girls, the total increase is 6├Ч4=24 months. Convert 24 months to years (2 years) and add it to the replaced girl's age: 12+2=14 years.
Students often forget to convert the increase in months (4 months) into years (4/12=1/3 years) or multiply the number of months by the number of people incorrectly.
Calculate total age increase
Calculate the total increase in months by multiplying the number of girls by the increase per girl.
6├Ч4=24┬аmonths
Convert months to years
Convert the total increase from months to years as the original age is in years.
24┬аmonths=1224тАЛ=2┬аyears
Find the new girl's age
Add the total increase to the age of the girl who was replaced.
12+2=14┬аyears
C is correct because the new girl is 14 years old, calculated by adding the total 2-year increase to the replaced 12-year-old's age.
This logic is identical to 'gain/loss' problems in Profit and Loss where the 'average' corresponds to the 'cost price' per unit.
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