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A Sum of Rs 700 is to Be Used to Give Seven Cash Prizes to Students of a School for Their Overall Academic Performance. - CBSE Class 10 - Mathematics

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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.

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.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 5: Arithmetic Progressions
Ex. 5.30 | Q: 16 | Page no. 113
 NCERT Solution for Mathematics Textbook for Class 10 (2018 to Current)
Chapter 5: Arithmetic Progressions
Ex. 5.30 | Q: 16 | Page no. 113
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. Concept: Sum of First n Terms of an AP.
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