In a cricket tournament 16 school terms participated. A sum of Rs8000 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 received is

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Rs.720

Rs.725

Rs.735

Rs. 780

answer is B.

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Detailed Solution

Here, $n = 16, S_{n} = 8000$

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

$a = 275$

Let common difference be d.

$\begin{array}{l} ∵ S_{n} = \frac{n}{2} [2 a + (n - 1) d] \\ ∴ 8000 = \frac{16}{2} [2 \times 275 + (16 - 1) d] \\ \Rightarrow 1000 = (550 + 15 d) \\ \Rightarrow 15 d = 450 \\ \Rightarrow d = 30 \\ Now, T_{16} = 275 + (16 - 1) 30 \\ = 275 + 450 \\ = 725 \end{array}$