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

1.	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» 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.

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»

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.