cat 2023 Question 12

Question

There are three persons A,B and C in a room. If a person D joins the room, the average weight of the persons in the room reduces by x kg. Instead of D, if person E joins the room, the average weight of the persons in the room increases by 2x kg. If the weight of E is 12 kg more than that of D, then the value of x is

Accepted Answer

Let us assume that A, B, C, D, and E weights are a, b, c, d, and e.

1st condition

$ \frac{(a+b+c)}{3} - \frac{(a+b+c+d)}{4} = x $

2nd condition

$ \frac{(a+b+c+e)}{4} - \frac{(a+b+c)}{3} = 2x $

Adding both the equations, we get:

$ \frac{(e-d)}{4} = 3x $

=> $ \frac{(e-d)}{4} = 3x $ => e - d = 12x

Given that 12x = 12 => x = 1.

Question 12.

Question Explanation