Question

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

Answer 1

Let the value of the first prize be ₹a.

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

∴ d = −₹20

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

Total sum of the prizes, S₇ = ₹700

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

$$\begin{gathered} S_7=\frac{7}{2}\left[2a+\left(7-1\right)\times \left(-20\right)\right]=700 \\ \Rightarrow \frac{7}{2}\left(2a-120\right)=700 \\ \Rightarrow 7a-420=700 \\ \Rightarrow 7a=700+420=1120 \end{gathered}$$
$\Rightarrow a=160$

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

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