0
The average of marks scored by the students of a class is 70. The average of marks of the girls in the class is 80 and that of boys is 60. What is the percentage of girls in the class?
- A70%
- B60%
- C50%
- D40%
Answer not set
Discussion 1
Log in or create a free account to reply and vote.
0
CCommunity
Average = sum of quantities/Total number of quantities
Let the number of boys and girls be ‘a’ and ‘b’ respectively.
Given, average of marks of the girls in the class is 80 and that of boys is 60.
∴ Total marks = 80b + 60a
Average marks of the whole class $(= \frac{{60a + 80b}}{{a + b}})$
Given, average marks = 70
$(\therefore \frac{{60a + 80b}}{{a + b}} = 70)$
⇒ 60a + 80b = 70a + 70b
⇒ 10a = 10b
⇒ a = b
Thus, number of boys and girls are equal.
∴ % of girls in class $(= \frac{b}{{b + a}} \times 100\% = \frac{b}{{2b}} \times 100\%)$
⇒ % of girls in class = 50%
Let the number of boys and girls be ‘a’ and ‘b’ respectively.
Given, average of marks of the girls in the class is 80 and that of boys is 60.
∴ Total marks = 80b + 60a
Average marks of the whole class $(= \frac{{60a + 80b}}{{a + b}})$
Given, average marks = 70
$(\therefore \frac{{60a + 80b}}{{a + b}} = 70)$
⇒ 60a + 80b = 70a + 70b
⇒ 10a = 10b
⇒ a = b
Thus, number of boys and girls are equal.
∴ % of girls in class $(= \frac{b}{{b + a}} \times 100\% = \frac{b}{{2b}} \times 100\%)$
⇒ % of girls in class = 50%