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 ofthe smallest and the greatest of the given numbers?

Let the number are a, b and c

According to question, 

$$\frac{a+b}{2}+c=68$$

• $$a+b+2c=136$$..................(i)

$$a+\frac{b+c}{2}=74$

• $$2a+b+c=148$$.................(ii)

$$b+\frac{a+c}{2}=98$$

• $$2b+a+c=196$$.................(iii)

Adding (i), (ii) and (iii), we get

4a + 4b + 4c  = 480

Divide it  by 4, 

a + b + c = 120..............(iv)

From (i), (ii), (iii) and (iv), 

First number , a = 148 - 120 = 28

Second number , b = 196 - 120 = 76

Third number , c = 136 - 120 = 16

Now, The average of smallest and greatest = $$\frac{76+16}{2}=\frac{92}{2}=46$$

Hence, Option A is correct.