Question

In a cricket tournament 16 school teams participated.A sum of Rs 8000 is to be awarded among themselves as prize miney.If the last placed team is awarded Rs 275 in prize money and the award increases by the same amount for successive finishing places,how much amount will the first place team receive?

Answer 1

Solution: The award increases by the same amount for successive finishing places, hence the resulting series will be an arithmetic progression

We know that the total prize money is 8000.

Therefore sum = 8000

Number of terms (n) is 16

First term (a) = 275

common difference = d

sum = $\frac{n}{2} (First-term +last-term)$

Here the last term will the amount which first ranked team will win

8000 = $\frac{16}{2}(275 + a)$

1000 = $275 + a$

a = 1000 -275 =725

Hence the first ranked team will win 725