Question

In a cricket tournament 16 school teams participated. A sum of Rs.16000 is to be awarded among themselves as prize money. If the team in the last place is awarded RS 550 in prize money and the award increases by the same amount for successive finishing places, how much amount will the team in the first place receive?

Answer 1

Let the first place team receive Rs a and let the award increase by Rs d. Then, these prizes form an AP in which first term = a, common difference = d, $T_{16}=550$ and $S_{16}=16000$

Now, $T_{16}=550\Rightarrow a+15d=550$ . . .. (i)

And, $S_{16}=16000\Rightarrow \frac{16}{2}\times [2a+15d]=16000$

$\Rightarrow$ 2a + 15d = 2000. . . . (ii)

On subtracting (i) from (ii), we get a = 1450.

Hence, the team in the first place receives Rs 1450.