Question 56
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
Solution
Let us assume that A, B, C, D, and E weights are a, b, c, d, and e.
1st condition
$$\dfrac{\left(a+b+c\right)}{3}-\dfrac{\left(a+b+c+d\right)}{4}=x$$
2nd condition
$$\dfrac{\left(a+b+c+e\right)}{4}-\dfrac{\left(a+b+c\right)}{3}=2x$$
Adding both the equations, we get:
$$\dfrac{\left(e-d\right)}{4}=3x$$
=> $$\dfrac{\left(e-d\right)}{4}=3x$$ => e - d = 12x
Given that 12x = 12 => x = 1.
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