A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance.

Solution:

Let the Ist prize be of Rs. a.

Then the next prize will be of Rs. (a – 20)

Then the next prize will be of Rs. {(a – 20) – 20},

i.e., Rs. (a – 40)

Thus, the seven prizes are of Rs. a, Rs. $(a-20)$, Rs. $(a-40), \ldots($ an AP)

Then $a+(a-20)+(a-40)+\ldots$ to 7 terms $=700$

$\Rightarrow \frac{7}{2}\{2 \mathrm{a}+6 \times(-20)\}=700 \quad(\because \mathrm{d}=-20)$

$\Rightarrow \frac{7}{2} \times(2 \mathrm{a}-120)=700 \Rightarrow \mathrm{a}-60=100$

$\Rightarrow a=160$

Thus, the 7 prizes are of Rs. 160 , Rs. 140 , Rs. 120 , Rs. 100 , Rs. 80 , Rs. 60 , Rs. 40 .