A girl aged 20 years left the class and in place of her a new boy joined the class. If the average of the class has decreased by 6 months, find the age of the new boy who joined the class if the total number of students in the class is 28.?

Question

A girl aged 20 years left the class and in place of her a new boy joined the class. If the average of the class has decreased by 6 months, find the age of the new boy who joined the class if the total number of students in the class is 28.?

4 years
5 years
6 years
7 years
8 years

LohaHridoy

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2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 3 : 6 years

Given:

Total number of students in the class = 28

Age of girl who left the class = 20 years

Average of the class decreased by 6 months

Formula used:

Average = Sum of Terms/Number of terms

Calculation:

Let the sum of the age of 28 students be x

Average of 28 students = x/28

Now, a girl of 20 years left the class and a new boy joined

Age of new boy be y

Sum of 28 students = x – 20 + y

New average of 28 students = (x – 20 + y)/28

Now, x/28 – (x – 20 + y)/28 = 6 months

⇒ (x/28) – (x – 20 + y)/28 = 1/2 year

⇒ (x – x + 20 – y)/28 = 1/2 year

⇒ (20 – y) = 14 years

⇒ y = 6 years

∴ Age of new boy is 6 years

Alternate Solution:

Total number of students in the class = 28

Average decreased by 6 months or 1/2 year

Age of girl who left = 20 years

Age of boy who joined = (20 – (28 × 0.5)

⇒ (20 – 14) years

⇒ 6 years

∴ Age of new boy is 6 years