CAT 2023 Slot 3 Solved Paper

Question : 56 of 66

Marks: +1, -0

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

2 x {\kg}

. If the weight of

E

12 {\kg}

more than that of

D

, then the value of

x

Solution:

Let us assume that

A, B, C, D

, and E weights are

a, b, c, d

, and e.
1st condition

\;{(a+b+c)}/{3}-\;{(a+b+c+d)}/{4}=x

2nd condition

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

Adding both the equations, we get:

\;\;{(e-d)}/{4}=3 x

\;⇒\;{(e-d)}/{4}=3 x ⇒e - d = 12 x

Given that

12 x=12⇒x=1

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