Question

In a cricket team tournament 16 teams participated. A sum of Rs 8000 is to be awarded among themselves as prize money. If the last place 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 first place term got Rs. A.
Since , award money increase by the same amount for successive finshing places .
Therefore seies is an AP.
Let the constant amount be d.
Here l=275,n=16and `s_(16)=8000`
` therefore l=a+(n-1)d`
`implies l=a+(16-1)(-d)`
[ we take common difference (-ve ) because saeies is decreasing ]
`implies 275 = a-15d`
and `S_(16)=(16)/(20[2a+(n-1).(-d)]`
`implies 8000=8[2a+(16-1) (-d)]`
`implies 8000=8[2a-15d]`
`implies 1000=2a-15d`
On subtracting Eq (i) from Eq (ii) we get
`(2a-15d)-(a-15d)=1000-275`
` implies 2a-15d-a +15d=725`
` therefore a=725`
Hence first palce terms receive Rs. 725.