# 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

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

**Solution:**

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 S_{n} = n/2 [2a + (n - 1) d] or S_{n} = 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 1st prize be x.

The cost of 2nd prize = x - 20

The cost of 3rd prize = x - 40

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, S_{7} = 700

By using the formula S_{n} = 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.

**Video Solution:**

## 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 Maths NCERT Solutions - Chapter 5 Exercise 5.3 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

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 then the value of each of the prizes was Rs 160, Rs 140, Rs 120, Rs 100, Rs 80, Rs 60, and Rs 40