# Average Marks Problem

The Average Marks Problem is as follows

Question :

Anjali, Bharti and Divya are the 3 smartest girls in the class. In a class test, the average marks of Anjali and Bharti is 80. The average of Bharti and Divya is 85, and the average of Divya and Anjali’s marks is 90. How much did Bharti score ? 😉

Solution :

First step is to write down the 3 equations.

Let us denote Anjali by A , Bharti by B and Divya by D .

So now since we know that the average of x and y is (x + y)/2 , let us now write the 3 equations. So we have…

(A + B)/2 = 80  ——-> A + B =160         …….eqn(1)

(B + D)/2 = 85  ——-> B + D =170          …….eqn(2)

(D + A)/2 = 90 ——-> D +  A =180        …….eqn(3)

S0, now from eqn (3),  we can write A = 180 – D    …….eqn(4)

But from equation (2) , D = 170 – B ….eqn (5)

Substitute eqn (5) in eqn (4) … so we get A = 180 – 170 +B  = 10 + B …….eqn(6)

Now put the value of A from eqn (6) in equation (1) , so

10 + B + B = 160

2B = 150

=> B = 75 Hence the correct answer is (d) 75 marks