Question

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?

Answer 1

Let the prize amount got by first-place team be ₹ a

Since, the prize money increases by the same amount for successive finishing places

Therefore the series will be A.P

∴ a_n = 275

n = 16

And S₁₆ = 8000

275 = a + (16 – 1)(– d)   ....[∵ Common difference d is (–) as the series is decreasing]

⇒ 275 = a – 15d  ....(i)

Now S_n = `n/2[2a + (n - 1)d]`

S₁₆ = `16/2 [2a + 15(-d)]`

⇒ 8000 = 8[2a – 15d]

⇒ 2a – 15d = 1000  ....(ii)

Solving equation (i) and equation (ii) we get

a = 725 and d = 30

Hence, the required award received by first place term = ₹ 725.