Question

A sum of$Rs700$ is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is $Rs20$ less than its preceding prize, find the value of each of the prizes.

Answer 1

Given that

A sum of $₹700$ is to be used to give seven cash prizes to students of a school for their overall academic performance. Each prize is$Rs20$ less than the preceding prize.

Find out

We have to find out the value of each of the prizes.

Solution

Let the cost of 1st prize be $Rs.P.$

Cost of 2nd prize$=Rs.P-20$

And the cost of the 3rd prize$=Rs.P-40$

We can see that the cost of these prizes are in the form of A.P., having common difference as$-20$ and first term as$P.$

Thus, $a=P$ and $d=-20$

Given that, $S_7$ $=700$

We know that the formula of the sum of nth term,

$S_n=\frac{n}{2}[2a+(n–1\left)d\right]$

$$\begin{gathered} \frac{7}{2}[2a+(7–1\left)d\right]=700 \\ \frac{[2a+(-6\left)\right(-20\left)\right]}{2}=\frac{700}{7} \end{gathered}$$

$$\begin{gathered} a+3(-20)=100 \\ a-60=100 \\ a=160 \end{gathered}$$

Therefore, the value of each of the prizes was $Rs160,Rs140,Rs120,Rs100,Rs80,Rs60,andRs40.$