Question

Question 16 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.

Class 10 - Math - Arithmetic Progressions Page 113

Answer 1

Solution:

Suppose the value of 1st prize be P.
value of 2nd prize = P − 20
 value of 3rd prize = P − 40

 The value of these prizes are in an A.P. having common difference(d) as −20 and first term(a) as P.

a = P
d = −20

Given ,

 S7 = 700

7/2 [2a + (7 – 1)d] = 700

a + 3(−20) = 100

a − 60 = 100

a= 100+60

a = 160
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Hence, the value of each of the prizes was Rs 160, Rs 140, Rs 120, Rs 100, Rs 80, Rs 60, and Rs 40.

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hope this will help you....

Answer 2

Let the cost of 1st prize be P.
Cost of 2nd prize = P − 20
And cost of 3rd prize = P − 40
It can be observed that the cost of these prizes are in an A.P. having common difference as −20 and first term as P.
a = P
d = −20
Given that, S7 = 700
7/2 [2a + (7 - 1)d] = 700

[2a+ (6)(-20)] / 2 = 100

a + 3(−20) = 100
a − 60 = 100
a = 160
Therefore, the value of each of the prizes was Rs 160, Rs 140, Rs 120, Rs 100, Rs 80, Rs 60, and Rs 40.