QUESTION

CSAT

Easy

Maths

Prelims 2013

A sum of Rs. 700 has to be used to give seven cash prizes to students in a school for their overall academic performance. Each prize is Rs. 20 less than its preceding prize.

What is the least value of the prize?

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Explanation

Let the value of the highest prize be x. The sequence of the seven prizes will be:

x,x20,x40,x60,x80,x100,x120x, x - 20, x - 40, x - 60, x - 80, x - 100, x - 120.

The sum of these prizes is given as Rs. 700, so:

x+(x20)+(x40)+(x60)+(x80)+(x100)+(x120)=700x + (x - 20) + (x - 40) + (x - 60) + (x - 80) + (x - 100) + (x - 120) = 700.

Simplifying the equation:

7x(20+40+60+80+100+120)=7007x - (20 + 40 + 60 + 80 + 100 + 120) = 700,

7x420=7007x - 420 = 700.

Now, solve for x:

7x=700+420=11207x = 700 + 420 = 1120,

x=1120/7=160x = 1120 / 7 = 160.

So, the highest prize is Rs. 160. The least prize will be:

160120=40160 - 120 = 40.

Thus, the least value of the prize is:

Rs. 40.

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