Question

In a cricket team tournament 16 teams participated. A sum of Rs. 8000 is to be awarded among themselves as prize money. If the last place 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

We have,

The total sum of prize money to be awarded among 16 teams, $S_{16}=Rs.8000$ and

the prize money awarded to the last place team i.e., $a_{16}=Rs.275$

As, the award increases by the same amount for successive finishing places.

So, the prize money are in A.P.

Let the prize money awarded to the first team be a.

Now, $S_{16}=8000$

$\Rightarrow \frac{16}{2}[a+a_{16}]=8000$

$\Rightarrow 8[a+275]=8000$

$\Rightarrow a+275=\frac{8000}{8}$

$\Rightarrow a=1000-275$

$\therefore a=725$

So, the amount which the first place team will receive is Rs. 725.