A sum of Rs 700 is to be used 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 of each of the prizes.
Step-by-Step Solution
Key Concept: Model the seven prizes as an AP with common difference -20, and use the given total as the sum of 7 terms.
Let the prizes (in decreasing order) form an AP with first term $a$ and $d=-20$, with $n=7$. Given $S_7=700$. [1.0 Mark]
$S_7=\dfrac72[2a+6(-20)]=700\Rightarrow2a-120=200\Rightarrow2a=320\Rightarrow a=160$. [1.0 Mark]
The seven prizes are $160,140,120,100,80,60,40$ (rupees). [1.0 Mark]
Correct Answer: