Question

A sum of rupees 2800 is to be used to give four cash prizes to students of a school for their over all acadmic performance . if each prize is rupees 200 less than its preceding prize , find the value of each prize .

Answer 1

Hi Sadhna,

let x be the highest prize money among all.

so we have

x+(x-200)+(x-400)+(x-600)= 2800
4x-1200 = 2800
4x = 4000
x = 1000

so the cash prizes given are
x, x-200, x-400, x-600
= 1000 Rs , 800 Rs  ,  600 Rs & 400Rs

Hope it helped.
Let me know if any further doubt.
Cheers !!!

Answer 2

Using AP,

Total sum of rupees =2800

Sn=n/2[2a+(n-1)d] eq:1
Sn=2800

n=4
d=200
a=?(4th prize)

Putting values in eq:1

4/2[2a(4-1)200]=2800
2[2a+600]=2800
4a+1200=2800
4a=1600
a=400

So fourth prize is 400rs
Third prize =a+d=400+200=600 rs
Second prize =a+2d=400+400=800 rs
First prize =a+3d=400+600=1000 rs