CAT 2023 Slot 3 QA Question & Solution
ArithmeticEasy
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
Options
2
0.5
1
1.5
Solution
Let us assume that A, B, C, D, and E weights are a, b, c, d, and e.
1st condition
$\frac{\left(a+b+c\right)}{3}-\frac{\left(a+b+c+d\right)}{4}=x$
2nd condition
$\frac{\left(a+b+c+e\right)}{4}-\frac{\left(a+b+c\right)}{3}=2x$
Adding both the equations, we get:
$\frac{\left(e-d\right)}{4}=3x$
=> $\frac{\left(e-d\right)}{4}=3x$ => e - d = 12x
Given that 12x = 12 => x = 1.