# A Sum of Rs 700 is to Be Used to Give Seven Cash Prizes to Students of a School for Their Overall Academic Performance. - Mathematics

Sum

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.

#### Solution 1

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

#### Solution 2

In the given problem,

Total amount of money (Sn) = Rs 700

There are a total of 7 prizes and each prize is Rs 20 less than the previous prize. So let us take the first prize as Rs a.

So, the second prize will be Rs a - 20  , third prize will be Rs a - 20 - 20 .

Therefore, the prize money will form an A.P. with first term a and common difference −20.

So, using the formula for the sum of n terms,

S_n = n/2 [ 2a + (n-1) d]

We get,

700 = 7/2 [ 2(a) + (7 - 1) (-20)]

700 = 7/2 [ 2a +(6) (-20)]

700 = 7/2 (2a - 120)

700 = 7 (a -60)

On further simplification, we get,

700/7 =  a - 60

100 + 60  = a

a = 160

Therefore, the value of first prize is Rs 160.

Second prize = Rs 140

Third prize = Rs 120

Fourth prize = Rs 100

Fifth prize = Rs 80

Sixth prize = Rs 60

Seventh prize= Rs 40

So the values of prizes are

Rs 160,RS 140,Rs 120,Rs 100,Rs 80,Rs 60,Rs 40.

Concept: Sum of First n Terms of an AP
Is there an error in this question or solution?

#### APPEARS IN

NCERT Class 10 Maths
Chapter 5 Arithmetic Progressions
Exercise 5.3 | Q 16 | Page 113
RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.6 | Q 69 | Page 55