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

In a cricket tournament 16 school teams participated. A sum of Rs 8000 is to be awarded among themselves as prize money. 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?

Answers (1)

Let the amount received by first place be Rs. A and ‘d’ be the difference in the amount. The last team receives Rs. 275. As there are 16 teams and all teams are given prizes hence the sequence will have 16 terms because there are 16 teams.

As total prize given is of 8000 rs hence

a+a-d+a-2d....+275 =8000

\\ n=16 \\\\ S_{16}=8000 \\\\ S_{n}= \left( \frac{n}{2} \right) \left( 2a+ \left( n-1 \right) (-d) \right) \\\\ 8000= \left( \frac{16}{2} \right) \left( 2a+ \left( 16-1 \right) (-d) \right) =8 \left( 2a-15d \right) \\\\ 1000=2a-15d \\\\ t_{16}=275 \\\\ t_{16}=a+ \left( 16-1 \right) (-d) \\\\ 275=a-15d \\\\ 1000-275= \left( 2a-15d \right) - \left( a-15d \right) \\\\ a=725 \\\\

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