Q. 164.4( 218 Votes )

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 10th NCERT - Mathematics 5. Arithmetic Progressions

Answer :

As, each price is decreased by 20 rupees, we can consider amount given to each student in increasing order to be an AP.
Let the lowest price given be 'a' and then prize is increased by Rs 20.
In that case, we have
First term = a
Common difference, d = - 20
No of terms, n = No of students getting prize = 7
Sum of 'n' terms = Total prize money = 700

Now,

we know, sum of 'n' terms on AP is

⇒ 700 × 2 = 7[2a - 120]
⇒ 200 = 2a - 120
⇒ 2a = 200 + 120
⇒ 2a = 320
⇒ a = 160
Hence, the divisions are Rs. 160, Rs. 140, Rs. 120, Rs. 100, Rs. 80, Rs. 60, Rs. 40

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

PREVIOUSA contract on construction job specifies a penalty for delay of completion beyond acertain date as follows: Rs 200 for the first day, Rs 250 for the second day, Rs 300 for the third day, etc., the penalty for each succeeding day being Rs 50 more than for thepreceding day. How much money the contractor has to pay as penalty, if he has delayedthe work by 30 days?NEXTIn a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, e.g., a section of Class I will plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?

Related Videos