Question

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

Answer 1

Let the first place team got Rs. $a$

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

$\therefore$ Series formed in A.P.

Let the constant amount be Rs. d

Now $I=275$, $n=16$ and $s_{16}=8000$

$\therefore 1=a+(n-1)d$

$275=a+15d$ …….$\left(1\right)$

$s_{16}=\frac{16}{2}[2a+15d]$

$8000=8[2a+15d]$

$\Rightarrow 1000=2a+15d$ ……..$\left(2\right)$

On substracting $\left(1\right)$ from $\left(2\right)$ we get,

$(2a+15d)-(a+15d)=1000-275$

$\Rightarrow a=725$

Hence, Rs. $725$ is received by first place team.