Question

A sum of Rs. 700 has to be used to give seven cash prizes to the students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, what is the least value of the prize?
1. Rs. 30
2. Rs. 40
3. Rs. 60
4. Rs. 80

Answer 1

Correct Answer - Option 2 : Rs. 40

Given:

Total sum S₇ = Rs. 700

Each prize is Rs. 20 less than its preceding prize

Formula used:

S_n = (n/2)[2a + (n - 1)d]

Where, S_n = sum of first n terms, a = first term, d = common difference, n = number of terms

Calculation:

Let the value of 1st prize be x

According to the question,

Value of 2nd prize = x - 20

Value of 3rd prize = x - 40

Similarly, we can write the values of seven prizes are

x, x - 20, x - 40,  x - 60, x - 80, x - 100, x - 120

Now, it can be observed that the values of these prizes in an A.P.

Here, a = x, d = -20 and n = 7

S₇ = (n/2)[2a + (n - 1)d]

700 = (7/2)[2 × x + (7 - 1) × (-20)]

⇒ 200 = [2x + 6 × (-20)]

⇒ 200 = 2x - 120

⇒ 320 = 2x

⇒ x = 160

Least value of the price = x - 120

⇒ 160 - 120

⇒ Rs. 40

∴ The least value of the prize is Rs. 40.