There are three persons $\mathrm{A}, \mathrm{B}$ 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 $2 \mathrm{x} \mathrm{kg}$. If the weight of $E$ is $12 \mathrm{~kg}$ more than that of $D$ , then the value of $x$ is

CAT 2023 Slot 3 QA Question 12

Multiple choice (+3 / −1) · Arithmetic · Mean, Median & Mode · Try it, then check the answer and solution below.

CAT 2023 Slot 3QAArithmetic • Mean, Median & ModeModerate

There are three persons

\mathrm{A}, \mathrm{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

joins the room, the average weight of the persons in the room increases by

2 \mathrm{x} \mathrm{kg}

. If the weight of

is

12 \mathrm{~kg}

more than that of

D , then the value of

x

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⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution

Official Convenor Answer Key: B

Answer and solution

Answer: B) $1$

📌 Core Concept

The average weight is calculated as the total weight divided by the number of individuals. When a new person joins, the total weight changes, affecting the average.

🔢 Step-by-Step Solution

Define Variables:

Let the total weight of A, B, and C be

T

Let the weight of D be

D

and E be

E = D + 12

Initial Average:

Average weight of A, B, C:

\frac{T}{3}

When D Joins:

Total weight:

T + D

Number of people:

- New average:

\frac{T + D}{4}

Given:

\frac{T + D}{4} = \frac{T}{3} - x

When E Joins:

Total weight:

T + E = T + D + 12

Number of people:

- New average:

\frac{T + D + 12}{4}

Given:

\frac{T + D + 12}{4} = \frac{T}{3} + 2x

Subtract the Two Equations:

\frac{T + D + 12}{4} - \frac{T + D}{4} = \left( \frac{T}{3} + 2x \right) - \left( \frac{T}{3} - x \right)

Simplify:

\frac{12}{4} = 3x \implies 3 = 3x \implies x = 1

⚡ 30-Second Shortcut

The difference in total weight (12 kg) causes a 3 kg change in average (from -1x to +2x). Thus,

12 = 3 \times 4 \implies x = 1

🎯 Final Answer

Correct Answer: B

CAT 2023 Slot 3 QA Question 12

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