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Given: Total teams in tournament are 16

Total prize money is Rs 8000

The last placed team is awarded Rs. 275

To find: Amount received by first place team

As the award money is increased by the same amount for successive finishing place, it forms an A.P.

Let a is amount receievd by first place team and d is successive increase in award

A.P. will be a, a + d, a + 2d,……………………

According to question:

n = 16, S16 = 8000 and a16 = 275

Formula used:

an = a + (n – 1)d

where a is first term, d is common difference and n is number of terms in an A.P.

Therefore,

a16 = a + (16 – 1)d

275 = a + 15d

a = 275 – 15d …………(1)

1000 = 2a + 15d …………(2)

Now put the value of a from (1) in (2):

1000 = 2(275 – 15d) + 15d

1000 = 550 – 30d + 15d

1000 = 550 – 15d

15d = 550 – 1000

15d = –450

d = -30

Put d = -30 in (1):

a = 275 – 15(-30)

a = 275 + 450

a = 725

Hence, amount received by first placed team is Rs. 725

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