Question

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.

Answer 1

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, S_n = \(\frac{n}{2}\)[2a + (n-1)d]

700 = \(\frac{7}{2}\)[2a + (7-1)-20]

\(\frac{1400}{7}\) =2a + 6(-20)

2a  = 200 + 120

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.