# A sum of ₹ 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ₹ 20 less than its preceding prize, find the value of each of the prizes.

**Solution:**

To find the value of each prize, we will use algebraic expressions and find their sum using the formula Sₙ = n/2 [2a + (n - 1) d]

7 cash prizes are given, and each prize is Rs. 20 less than its preceding prize.

The sum of the first n terms of an AP is given by Sₙ = n/2 [2a + (n - 1) d] or Sₙ = n/2 [a + l].

Here, a is the first term, d is a common difference and n is the number of terms.

Let the cost of the 1^{st} prize be x

The cost of 2^{nd} prize = x - 20

The cost of 3^{rd} prize = x - 40

Thus, the prizes are x, (x - 20), (x - 40),...

By observation, costs of these prizes are in an A.P., having common difference as - 20 and first term as x.

a = x, d = - 20

Given that, S₇ = 700

By using the formula Sₙ = n/2 [2a + (n - 1) d]

7/2 [2x + (7 - 1) d] = 700

7 [2x + (6) × (- 20)] = 700 × 2

[2x + (6) × (- 20)] = 1400 / 7

[2x + (6) × (- 20)] = 200

x + 3 × (- 20) = 100

x - 60 = 100

x = 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.

**☛ Check: **NCERT Solutions Class 10 Maths Chapter 5

**Video Solution:**

## A sum of ₹ 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ₹ 20 less than its preceding prize, find the value of each of the prizes

Class 10 Maths NCERT Solutions Chapter 5 Exercise 5.3 Question 16

**Summary:**

A sum of ₹ 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ₹ 20 less than its preceding prize then the value of each of the prizes was ₹ 160, ₹ 140, ₹ 120, ₹ 100, ₹ 80, ₹ 60, and ₹ 40.

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