The ratio of number of girls to number of boys is 3 : 2 in a class of 60 students. The average marks scored by the boys in Physics is 72 and the average marks scored by the whole class in Physics is 81. What is the average marks in Physics scored by girls?

Correct option is D

Given:

The ratio of number of girls to boys = 3 : 2.

Total number of students = 60.

Average marks scored by boys = 72.

Average marks scored by the whole class = 81.

Formula Used:

Total marks scored by the whole class = Average marks of the whole class × Total number of students.

Total marks scored by boys = Average marks of boys × Number of boys.

Solution:

Let the number of boys = x, and the number of girls =$$\frac{3}{2 } x.$$​​

Given that the total number of students = 60, we can write:
x +$$\frac{3}{2}x$$​= 60
​$$\frac{5}{2}x = 60 \quad \implies \quad x = 24 \text{ (boys)}.$$​​
Therefore, the number of girls =$$\frac{3}{2} \times 24 = 36$$​​

The total marks scored by the whole class = $$81 \times 60 = 4860$$​​

The total marks scored by the boys = $$72 \times 24 = 1728$$​​

The total marks scored by the girls = 4860 - 1728 = 3132.

The average marks scored by girls =$$\frac{3132}{36} = 87 .$$​​

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