In a class having 40 boys and some girls, the average ages of boys and girls are 13.5 years and 13 years respectively. The average age of the whole class is 13.4 years. Then the number of girls in the class is?

Question

In a class having 40 boys and some girls, the average ages of boys and girls are 13.5 years and 13 years respectively. The average age of the whole class is 13.4 years. Then the number of girls in the class is?

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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 1 : 10

Given:

The number of boys = 40

The average age of boys = 13.5 years

The average age of girls = 13 years

The average age of the whole class = 13.4 years

Calculation:

Let the number of girls be x

According to the question. we have

The total ages of girl = 13x

The total ages of boys = 13.5 × 40

⇒ 540 years

The total number of students = 40 + x

Now,

The total ages of the whole class = The total ages of girl + The total ages of boys

⇒ 13.4 × (40 + x) = 13x + 540

⇒ 536 + 13.4x = 13x + 540

⇒ 13.4x - 13x = 540 - 536

⇒ 0.4x = 4

⇒ x = 10

∴ The number of girls in the class is 10.

Alternate Method

Calculation:

Allegation Method:

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⇒ 4 units = 40

⇒ 1 unit = 10

∴ The number of girls in the class is 10.