There are 3 students in a group. If the weight of any student is added to the average weight of the other two, the sums received are 48 kg, 52 kg, and 59 kg. The average weight (in kg) of the three students is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 26.5.
A + (B + C)/2 = 48 ⇒ 2A + B + C = 96 .....(1)
B + (A + C)/2 = 52 ⇒ 2B + A + C = 104 .....(2)
C + (A + B)/2 = 59 ⇒ 2C + A + B = 118 .....(3)
From (2) - (1) ⇒ (2B + A + C) - (2A + B + C) = 104 - 96
⇒ B = A + 8 .....(4)
From (3) - (2) ⇒ (2C + A + B) - (2B + A + C) = 118 - 104
⇒ C = B + 14 = A + 22 .....(5)
From (1) we get 2A + (A + 8) + (A + 22) = 96
⇒ 4A + 30 = 96
⇒ A = 16.5
⇒ B = 16.5 + 8 = 24.5
⇒ C = 24.5 + 14 = 38.5
Average = (16.5 + 24.5 + 38.5)/3 = 79.5/3 = 26.5 kg