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Question
In a cricket team tournament 16 teams participated. A sum of ₹8000 is to be awarded among themselves as prize money. If the last place team is awarded ₹275 in prize money and the award increases by the same amount for successive finishing places, then how much amount will the first place team receive?
Solution
We have,
the total sum of prize money to be awarded among 16 teams, S16 = ₹8000 and
the prize money awarded to the last place team i.e. a16 = ₹275
As, the award increases by the same amount for successive finishing places.
So, the prize money are in A.P.
Let the prize money awarded to the first team be a.
Now,
\[S_{16} = 8000\]
\[ \Rightarrow \frac{16}{2}\left[ a + a_{16} \right] = 8000\]
\[ \Rightarrow 8\left[ a + 275 \right] = 8000\]
\[ \Rightarrow a + 275 = \frac{8000}{8}\]
\[ \Rightarrow a = 1000 - 275\]
\[ \therefore a = 725\]
So, the amount which the first place team will recieve is ₹725.
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