CAT 2023 Slot 3 QA Question 10: 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

Question

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

Accepted Answer

Let the average weight of A, B and C be W. Then their total weight is $3W$.

When D joins, the new average is $W - x$.
$\dfrac{3W + D}{4} = W - x$
$D = W - 4x$

When E joins instead, the new average is $W + 2x$.
$\dfrac{3W + E}{4} = W + 2x$
$E = W + 8x$

Given $E - D = 12$,
$(W + 8x) - (W - 4x) = 12