Answer :

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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