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

Question:

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 prize.

Solution:

In the given problem,

Total amount of money (Sn) = Rs 700

There are a total of 7 prizes and each prize is Rs 20 less than the previous prize. So let us take the first prize as Rs a.

So, the second prize will be Rs, third prize will be Rs.

Therefore, the prize money will form an A.P. with first term a and common difference −20.

So, using the formula for the sum of n terms,

$S_{n}=\frac{n}{2}[2 a+(n-1) d]$

We get,

$700=\frac{7}{2}[2(a)+(7-1)(-20)]$

$700=\frac{7}{2}[2 a+(6)(-20)]$

$700=\frac{7}{2}(2 a-120)$

$700=7(a-60)$

On further simplification, we get,

$\frac{700}{7}=a-60$

$100+60=a$

$a=160$

Therefore, the value of first prize is Rs 160.

Second prize = Rs 140

Third prize = Rs 120

Fourth prize = Rs 100

Fifth prize = Rs 80

Sixth prize = Rs 60

Seventh prize= Rs 40

So the values of prizes are  Rs 160, Rs 140, Rs 120, Rs 100, Rs 80, Rs 60, Rs 40

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