Question

a sum of rs 2750 is to be distributed as 10 cash prizes , if each prize is 50 less than its preceeding prize. find the value if each prize?

Answer 1

here is a simple solution for your problem-
assume that the constant value given to each winner is 'x'.
and the variable or the added value given to each successive winner = rs.50
so, the 10 prizes are-  x , x-50, x-100, x-150, x-200, x-250, x-300, x-350,
                                   x-400 , x-450 
when we add all these terms we get
                    10x+(-50-100-150-200-250-300-350-400-450)=2750
                     10x+(-2250)=2750
                     10x=5000
                     x=500
Therefore the prizes are-
           1st prize=x=500
            2nd prize=x-50=450
            3rd prize = x-100=400
           4th prize=x-150=350
           5th prize=x-200=300
           6th prize=x-250=250
           7th prize=x-300=200
           8th prize=x-350=150
           9th prize=x-400=100
          10th prize=x-450=50