Discussion

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 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?

Explanation:

Let the old average be 'a'.
∴ Total weight of the three students = 3a

Let the weight of D and E be D kgs and E kgs respectively.

Because of D the average reduces by x kg.
⇒ a - x = (3a + D)/4
⇒ 4a - 4x = 3a + D
⇒ D = a - 4x ...(1)

Because of E the average increases by 2x kg.
⇒ a + 2x = (3a + E)/4
⇒ 4a + 8x = 3a + E
⇒ E = a + 8x ...(2)

We know, E - D = 12
⇒ (a + 8x) - (a - 4x) = 12
⇒ 12x = 12
⇒ x = 1

Hence, option (c).

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