A sum of ₹700 is to be used to give seven cash prizes to students of a school for their overall academic performance.
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.
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, $S_{n}=\frac{n}{2}[2 a+(n-1) d]$, we get
$S_{7}=\frac{7}{2}[2 a+(7-1) \times(-20)]=700$
$\Rightarrow \frac{7}{2}(2 a-120)=700$
$\Rightarrow 7 a-420=700$
$\Rightarrow 7 a=700+420=1120$
$\Rightarrow a=160$
Thus, the value of the first prize is ₹160.
Hence, the value of each prize is ₹160, ₹140, ₹120, ₹100, ₹80, ₹60 and ₹40.
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