NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 16

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 16

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 of the prizes.

Given:

Total sum = Rs 700
Number of prizes = 7
Each prize is Rs 20 less than its preceding prize.

To Find:

The value of each of the seven prizes.

Formula:

Arithmetic Progression sum formula: S = n2(a + l), where 

S is the sum, 

n is the number of terms, 

a is the first term, and 

l is the last term.

Solution:

Let the first prize be 'a'. 

Then the 7 prizes are a, a-20, a-40, a-60, a-80, a-100, a-120.

Sum of the A.P = S = n2 (a + l) = 700
⇒ 72(a + a - 120) = 700

⇒ 72(2a - 120) = 700
⇒ 7(2a - 120) = 1400
⇒ 2a - 120 = 200
⇒ 2a = 320
⇒ a = 160

Therefore, the prizes are: 160, 140, 120, 100, 80, 60, 40

Result:

The values of the prizes are Rs 160, Rs 140, Rs 120, Rs 100, Rs 80, Rs 60, and Rs 40.

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