Question

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

Answer 1

Let the 1st prize be a
So the 2nd prize = a - 20
The 3rd prize = (a - 20) - 20 = a - 40
And so on
So, the series will be a, a - 20, a - 40, ....
Since the difference is the same, it is an AP
Here, sum of Rs 700 is given,
So, $S_n$ = 700
Also, a = a
d = (a - 20) - a = a - 20 - a = -20
We know that
$S_n$ = $\frac{n}{2}$(2a + (n - 1)d)
Putting the values
700 =$\frac{7}{2}$ (2a + (7 - 1) x -20)
700 =$\frac{7}{2}$(2a + 6 x -20)
700 = $\frac{7}{2}$(2a - 120)
700 x $\frac{2}{7}$ = 2a - 120
200 = 2a - 120
200 + 120 = 2a
320 = 2a
a = 160
So, 1st prize = a = 160
2nd prize = a - 20 = 160 - 20 = 140
3rd prize = a - 40 = 160 - 40 = 120
4th prize = a - 60 = 160 - 60 = 100
5th prize = a - 80 = 160 - 80 = 80
6th prize = a - 100 = 160 - 100 = 60
7th prize = a - 120 = 160 - 120 = 40