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A class has 20 boys and 20 girls. The average age of girls in the class is 16 years and the average age of boys in the class is 17 years. One girl and one boy leave the class and the average age of the girls reduced by 1 year and that of boys reduced by 2 years. Find the new average age of the whole class.

A class has 20 boys and 20 girls. The average age of girls in the class is 16 years and the average age of boys in the class is 17 years. One girl and one boy leave the class and the average age of the girls reduced by 1 year and that of boys reduced by 2 years. Find the new average age of the whole class. Correct Answer 15 years

Given:

A class has 20 boys and 20 girls. 

The average age of girls in the class = 16 years

The average age of boys in the class = 17 years

Formula Used:

Sum of all numbers = Average of numbers × Number of terms

Calculation:

Sum of ages of girls = Average × Numbers of girls

⇒ 20 × 16

⇒ 320

Sum of ages of boys = Average × Numbers of boys

⇒ 20 × 17

⇒ 340

One girl and one boy leave the class so the number of boys is 19 and number of girls is 19.

The new average age of the girls = 16 – 1 = 15

The new average age of the boys = 17 – 2 = 15

The new sum of ages of girls = New average × Numbers of girls

⇒ 19 × 15

⇒ 285

The new sum of ages of boys = New average × Numbers of boys

⇒ 19 × 15

⇒ 285

Total new age of boys and girls = 285 + 285 = 570

New average of whole class = Sum of ages of all/total number of students

⇒ 570/38

⇒ 15

∴ The new average age of the whole class is 15 years.

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