Averages and Changes in Mean Weight

CAT 2023 Slot 3 · QA · Easy · Arithmetic

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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 xx kg. Instead of D, if person E joins the room, the average weight of the persons in the room increases by 2x2x kg. If the weight of E is 12 kg more than that of D, then the value of xx is

  1. A.

    1.5

  2. B.

    2

  3. C.

    0.5

  4. D.

    1

Answer

D

Explanation

Let S=A+B+CS = A + B + C. When D joins: S3−S+D4=x  ⟹  4S−3S−3D=12x  ⟹  S−3D=12x\frac{S}{3} - \frac{S+D}{4} = x \implies 4S - 3S - 3D = 12x \implies S - 3D = 12x

When E joins: S+E4−S3=2x  ⟹  3S+3E−4S=24x  ⟹  3E−S=24x\frac{S+E}{4} - \frac{S}{3} = 2x \implies 3S + 3E - 4S = 24x \implies 3E - S = 24x

Adding the two equations: (S−3D)+(3E−S)=12x+24x(S - 3D) + (3E - S) = 12x + 24x 3(E−D)=36x  ⟹  E−D=12x3(E - D) = 36x \implies E - D = 12x

Given E−D=12E - D = 12, we get: 12x=12  ⟹  x=112x = 12 \implies x = 1

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