Question

In a cricket team tournament 16 teams participated 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?

Answer 1

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 received 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 : 

a_n = a + (n – 1)d

S_n = \(\frac{n}{2}\){2a + (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 = \(\frac{-450}{15}\)

⇒ 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