Three numbers are such that when the average of any two of them is added to the third, the results obtained are 192, 180, and 168, respectively. What is the average of the original three numbers?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 90
Let the three numbers be x, y, and z
x + (y + z)/2 = 192
⇒ 2x + y + z = 384 .....(1)
y + (x + z)/2 = 180
⇒ 2y + x + z = 360 .....(2)
z + (x + y)/2 = 168
⇒ 2z + x + y = 336 .....(3)
(1) + (2) + (3) ⇒ 4x + 4y + 4z = 384 + 360 + 336 = 1080
⇒ x + y + z = 270
Average = 270/3 = 90