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# Question 69. 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.

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One of the most important and exam oriented question from Chapter name- Arithmetic Progression
Class 10th
Chapter number- 9
Exercise :- 9.6
This type of question has been asked in previous years exams.

In this question we have been given that a sum of Rs 700 is to be used to give seven cash prizes to students

Also it is given that each prize is Rs 20 less than its preceding prize,

Now we have to find the value of each prize.

CBSE DHANPAT RAI publication
CBSE Mathematics Class 10th
Question 69

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1. Total amount that has to be given(S7) = Rs 700

Number of Prizes(n) = 7

As each prize is Rs 20 less than its preceding prize,

these prizes are forming an A.P. with common difference(d) = –20

By using the formula of the sum of n terms of an A.P.

Sn = n[2a +(n – 1)d] / 2

=> 700 = 7[2(a) + (7 – 1)(–20)] / 2

=> 2a – 120 = 200

=> 2a = 320

=> a = 160

The value of 1st prize = 160

The value of 2nd prize = 160 – 20 = Rs 140

The value of 3rd prize = 140 – 20 = Rs 120

The value of 4th prize = 120 – 20 = Rs 100

The value of 5th prize = 100 – 20 = Rs 80

The value of 6th prize = 80 – 20 = Rs 60

The value of 7th prize = 60 – 20 = Rs 40

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