Q. 454.5( 8 Votes )

A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, find the value of each prize.

Answer :

Let the first prize be Rs. x. Thus each succeeding prize is Rs. 20 less than the preceding prize.

Second prize, third prize, …, seventh prize be Rs. (x - 20), (x - 40) , …, (x - 120).


This forms an AP as x, x - 20, …, x - 120.


Here, first term = x


Common difference = x - 20 - x = - 20


Total number of terms = 7


Since, Total sum of prize amount = 700.


Sum of all the terms = 700


Now, sum of first n terms of an AP is given by:


Sn = [2a + (n - 1)d]


Sum of 7 terms of an AP is given by:


S7 = [2a + (7 - 1)d] = 700


[2x + (7 - 1)(-20)] = 700


7[2x - 120] = 1400


2x - 120 = 200


x - 60 = 100


x = 160


Thus, the prizes are as Rs. 160, Rs.140, Rs.120, Rs. 100, Rs. 80, Rs. 60, Rs. 40.


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