Q. Consider the following data:
Girls’s Average marks in English = 9
Girls’s Average marks in Hindi = 8
Boys’s Average marks in English = 8
Boys’s Average marks in Hindi = 7
Overall Average marks in English = 8.8
What is the value of Overall Average marks in Hindi?
(a) 7.8
(b) 7.6
(c) 7.4
(d) 7.2
Correct Answer: (a) 7.8
Question from UPSC Prelims 2020 CSAT Paper
Explanation :
Overall Average marks in Hindi
Let’s assume that there are x girls and y boys in the class. From the given data we can write two equations:
The total marks in English for girls and boys combined is (9x + 8y), and the overall average marks in English is 8.8, so (9x + 8y)/(x+y) = 8.8.
The total marks in Hindi for girls and boys combined is (8x + 7y).
Solving equation (1) for x in terms of y, we get: x = 4y.
Substituting this value of x into the expression for total marks in Hindi, we get: (8(4y) + 7(y))/(4y+y) = (39y)/(5y) = 7.8.
So the overall average marks in Hindi is 7.8.
