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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, amount will the first-place team receive is

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Rs. 720

Rs. 725

Rs. 735

Rs. 780

answer is B.

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Detailed Solution

Given,
Number of terms

n = 16

Sum of the money awarded

S_{n} = 8000

First term

a = 275,

Suppose that,
The series formed in arithmetic progression
We know that the formula

S_{n} = \frac{n}{2} (a + l)

Where l is the last term of the series.
Put the value in the formula we obtain,

8000 = \frac{16}{2} (275 + l)

l = \frac{8000 \times 2}{16} - 275

l = 1000 - 275

l = 725

Hence the receiving money Rs. 725 of the first team.
Option 2 is correct.

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