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:
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:
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:
Options
Answer: 1
Explanation:
Problem: Three persons A, B, C in a room → average weight = W₀ = (A + B + C)/3 If D joins → average decreases by x → new average = W₀ − x If E joins → average increases by 2x → new average = W₀ + 2x Weight of E = weight of D + 12 Solution: Step 1: Express weights of D and E With D: (A + B + C + D)/4 = W₀ − x → D = 4(W₀ − x) − (A + B + C) = W₀ − 4x With E: (A + B + C + E)/4 = W₀ + 2x → E = 4(W₀ + 2x) − (A + B + C) = W₀ + 8x Step 2: Use E = D + 12 W₀ + 8x = W₀ − 4x + 12 → 12x = 12 → x = 1 Answer: 1
Explanation:
Problem: Three persons A, B, C in a room → average weight = W₀ = (A + B + C)/3 If D joins → average decreases by x → new average = W₀ − x If E joins → average increases by 2x → new average = W₀ + 2x Weight of E = weight of D + 12 Solution: Step 1: Express weights of D and E With D: (A + B + C + D)/4 = W₀ − x → D = 4(W₀ − x) − (A + B + C) = W₀ − 4x With E: (A + B + C + E)/4 = W₀ + 2x → E = 4(W₀ + 2x) − (A + B + C) = W₀ + 8x Step 2: Use E = D + 12 W₀ + 8x = W₀ − 4x + 12 → 12x = 12 → x = 1 Answer: 1
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