Question

A sum of 700 is to be issued 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 for each prize.

Answer 1

Let the value of the first prize be Rs. a

Since the value of each prize is Rs. 20 less than its preceding prize, so the values of the prizes are in AP with the common difference as Rs. -20

Therefore, d=−20

Number of the cash prize to be given to the students, n = 7

The total sum of the prizes, $S_7=Rs.700$

Using the formula, $S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
we get

$S_7=\frac{7}{2}[2\times a+(7–1)\times (-20\left)\right]=700$

$=\frac{7}{2}\times (2a–120)=700$
$=7a–420=700$

⇒$7a=700+420=1120$

⇒$a=160$

Thus, the value of the first prize is Rs. 160.

Hence, the value of each prize is Rs. 160, Rs. 140, Rs. 120,Rs. 100, Rs. 80, Rs. 60, and Rs. 40.