Question

In a cricket tournament 16 school teams participated. A sum of ₹ 1600 is to be awarded among themselves as prize money. If the team in the last place is awarded ₹ 500 in prize money and the award increases by the same amount for successive finishing places, how much amount will the team in the first place receive ?

Answer 1

Let the frist place team receive ₹ a and let the award increase by ₹ d. then, these prizes form an AP in which first term.= a , common difference=d, ` T_(16) = 550 and S_(16) = 16000`
Now, ` T_(16) = 550 Rightarrow a + 15 d = 550`
And, ` S_(16) = 16000 Rightarrow 16/2 xx [2a +15] = 16000`
` Rightarrow 2a + 15 d = 2000`
On subtracting (i) from (ii) , we get a = 1450
Hence, the team in the first place receives ₹ 1450 .