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CAT 2023 Slot 3 — QA Question 12

Change in AverageEasy

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?

Answer & solution

  • A

    1.5

  • B

    0.5

  • 1

  • D

    2

Solution

Easy

Translate each "average changes by..." statement into a total-weight equation for 4 people. That gives D and E in terms of the old average aa and xx. Then use "EE is 12 more than DD" — the aa terms cancel and xx pops out.

Let the old average of A, B, C be aa, so their total weight is 3a3a. Let D, E weigh DD and EE kg.

1

D joins ⇒\Rightarrow average falls by xx (now 4 people):

a−x=3a+D4⇒ 4a−4x=3a+D ⇒ D=a−4x\begin{aligned} &a-x=\frac{3a+D}{4}\\ &\Rightarrow\ 4a-4x=3a+D\ \Rightarrow\ D=a-4x \end{aligned}
2

E joins instead ⇒\Rightarrow average rises by 2x2x:

a+2x=3a+E4⇒ 4a+8x=3a+E ⇒ E=a+8x\begin{aligned} &a+2x=\frac{3a+E}{4}\\ &\Rightarrow\ 4a+8x=3a+E\ \Rightarrow\ E=a+8x \end{aligned}
3

Apply E−D=12E-D=12; the aa cancels:

(a+8x)−(a−4x)=12⇒ 12x=12 ⇒ x=1\begin{aligned} &(a+8x)-(a-4x)=12\\ &\Rightarrow\ 12x=12\ \Rightarrow\ x=1 \end{aligned}
x=1x=\mathbf{1}
CAT 2023 Slot 3 QA Q12: There are three persons A, B and C in a room. If a person D joins the room, the average weight of the persons — Solution | TheCATExam