Question

The average of next two numbers is 75. The average of first three numbers is 50. The average of next two numbers 75. The seventh number is 10 more than the sixth number and 10 less: than the eighth number. What is the average of the seventh and eighth number?​

Answer 1

Answer:

Step-by-step explanation:

Suppose the first three numbers be $x, y, z$

It is given that the average of first three numbers is $50$.

Therefore, we get

                              $\frac{x+y+z}{3} =50$

Suppose the next two numbers be $a, b$ respectively.

It is given that the average of next two numbers is $75$.

Therefore, we get

                               $\frac{a+b}{2} =75$

Suppose the sixth, seventh and eighth number be $s, t, u$ respectively.

It is given that seventh number is $10$ more than the sixth number and $10$ less than the eighth number.

Therefore, we get

                              $t=10+s$    and   $t+10=u$

Therefore, the average of seventh and eighth number will be

                                     $\frac{t+u}{2} =\frac{t+t+10}{2} \\\frac{t+u}{2} =\frac{2t+10}{2} \\\frac{t+u}{2} =\frac{2(t+5)}{2}\\\frac{t+u}{2} =t+5$

Therefore, the average of seventh and eighth number will be $5$ more than the seventh number.