Question:easy

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 kg x . If the weight of E is 12 kg more than that of D , then the value of x is

Updated On: Jan 13, 2026
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The Correct Option is C

Solution and Explanation

Let \( S \) represent the total weight of persons A, B, and C, and \( \frac{S}{3} \) their average weight.

When person D joins, the new average is \( \frac{S + w_D}{4} \), which is \( x \) kg less than the original average:

\(\frac{S}{3} - x = \frac{S + w_D}{4}\)

Multiplying by 12 gives:

\(4S - 12x = 3S + 3w_D\)

Simplifying yields:

\(S = 12x + 3w_D\)

If person E joins instead, the average increases by \( 2x \) kg:

\(\frac{S}{3} + 2x = \frac{S + w_E}{4}\)

Multiplying by 12 gives:

\(4S + 24x = 3S + 3w_E\)

Simplifying yields:

\(S = 24x + 3w_E\)

Equating the two expressions for \( S \):

\(12x + 3w_D = 24x + 3w_E\)

Dividing by 3 gives:

\(4x + w_D = 8x + w_E\)

Given \( w_E = w_D + 12 \), substitute into the equation:

\(4x + w_D = 8x + w_D + 12\)

Simplifying to solve for \( x \):

\(-4x = 12\)

Therefore, \( x = 1 \).

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