There are three positive numbers. If the average of any two of them is added to the third number, the sums obtained are 68, 74 and 98. What is the average of the smallest and the greatest of the given numbers?

46

Let three numbers are P , Q & R

ATQ ,

\(\frac{P+Q}{2}\) + R = 68

P + Q + 2R = 136 -----(1)

\(\frac{Q + R }{2}\) + P = 74

Q + R + 2P = 148   -----(2)

\(\frac{P + R }{2}\) + Q = 98

P + R + 2Q = 196    ----(3)

4 ( P + Q + R ) = 480

P + Q +  R = 120

By putting value of ( P + Q + R ) in eqn (1) , eqn(2) & (3)

P = 148 - 120 = 28

Q = 196 - 120 = 76

R = 136 - 120 = 16

Average of smallest and greatest numbers = \(\frac{16 + 76 }{2}\) = 46