In set of three numbers,the average of the first two numbers is 7, the average of the last two numbers is 10, and the average of the first and the last numbers is 14. What is the average of the three numbers?

Let the three numbers are a, b, c respectively

Given,

Average of the first two numbers = 7

$$=$$>  $$\frac{a+b}{2}=14$$

$$=$$>  $$a+b=28$$ ..........................(1)

Average of the last two numbers = 10

$$=$$>  $$\frac{b+c}{2}=10$$

$$=$$>  $$b+c=20$$ ..........................(2)

Average of the first and last number = 14

$$=$$>  $$\frac{a+c}{2}=14$$

$$=$$>  $$a+c=28$$ ..........................(3)

Adding (1), (2), (3)

$$2a+2b+2c=14+20+28$$

$$=$$>  $$2a+2b+2c=62$$

$$=$$>  $$a+b+c=31$$

Average of the three numbers = $$\frac{a+b+c}{3}$$ = $$\frac{31}{3}$$

Hence, the correct answer is Option A