Question

In a cricket tournment, 16 school 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 awarded increases by te same amount for successive finishing places, then how much amount will the first place team received? What value is shown in this question?

Answer 1

The total number of team participated in a cricket tournament n=16

The sum of money awarded as a prize money. $S_n=8000$

Since, we consider last place team as a first term, a =275

Let common difference be d.

$\because S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$\therefore 8000=\frac{16}{2}[2\times 275+(16-1\left)d\right]$

$\Rightarrow 1000=550+15d\Rightarrow 15d=450\Rightarrow d=30$

Now, $T_{16}=275+(16-1)30=275+450=725$

Hence, the first place team will bet prize Rs. 725

The value shown in this question is appreciating the efforts of each cricket team, either the bottom lever or top level, so that the bottom level will do a better performance in further tournament.