The average of 8 numbers is 20. The average of first two numbers is $$15\frac{1}{2}$$ and that of the next three is $$21\frac{1}{3}$$. If the sixth number be less than the seventh and eighth numbers by 4 and 7 respectively, then the eight number is-

Let the eight number be x
Then, sixth number = (x - 7)
Seventh number = (x - 7) + 4 = (x - 3)
So,
$$ \Leftrightarrow \left( {2 \times 15\frac{1}{2}} \right) + \left( {3 \times 21\frac{1}{2}} \right)$$     $$ + \left( {x - 7} \right)$$   $$ + \left( {x - 3} \right)$$   $$ + \,x = 8 \times 20$$
$$\eqalign{ & \Leftrightarrow 31 + 64 + \left( {3x - 10} \right) = 160 \cr & \Leftrightarrow 3x = 75 \cr & \Leftrightarrow x = 25 \cr} $$