The average of ten numbers is 32.5. The average of first four numbers is 25.6 and that of the last three numbers is 38.2. The 5th number is 50% more than the 6th number and 8 less than the 7th number. What is the average of 5th and 7th numbers?

41.5

Sum of all ten numbers = 10 x 32.5

Sum of First four numbers = 4 x 25.6

Sum of last three numbers = 3 x 38.2

So sum of 5th, 6th and 7th numbers = (10 x 32.5) - 4 x 25.6 -3 x 38.2 = 108

Let's assume 5th number is x

then 6th number is \(\frac{2}{3}\)x and 7th number is x + 8

From above,

x + \(\frac{2}{3}\)x + x + 8 = 108

x=  37.5

Accordingly, 5th number is 37.5 and 7th number is 45.5

Avg. of 5th and 7th number is = 41.5