In a cricket team tournment 16 teams particpated a sum of 8000 is to to awarded among themselves a price money. It the last placed team is awarded 275 in price money and the award increased by the same amount for successive finishing place , how much amount will the first place team receive?
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