A sum of Rs.700 is to be used to gives even 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.

Amount of money = 700

Total number of prize = 7


Each prize is Rs. 20 less than its preceding prize


Let, Prize of first prize = a


Prize of second prize = a – 20


Prize of third prize = a – 20 – 20 = a – 40


Here, A.P. is a, a – 20, a – 40,…


So, common difference, d = a – 20 – a = -20


We know, Sn = [2a + (n – 1) d]


700 = [2a + (7 – 1) -20]


= 2a + 6 (-20)



2a = 320


a = 160


So, value of first prize = 160


Value of second prize, 160 – 20 = 140


Value of third prize, 140 – 20 = 120


Value of fourth prize, 120 – 20 = 100


Value of fifth prize, 100 – 20 =80


Value of sixth prize, 80 – 20 = 60


And value of seventh prize, 60 – 20 = 40


Hence, value of prizes, Rs 160, Rs 140, Rs 120, Rs 100, Rs 80, Rs 60, Rs 40.


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