Check sibling questions

Ex 5.3, 16 - A sum of Rs 700 is to be used to give seven

Ex 5.3, 16 - Chapter 5 Class 10 Arithmetic Progressions - Part 2
Ex 5.3, 16 - Chapter 5 Class 10 Arithmetic Progressions - Part 3

This video is only available for Teachoo black users

Solve all your doubts with Teachoo Black (new monthly pack available now!)


Transcript

Ex 5.3, 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. Let the 1st prize be a So, 2nd prize = a – 20 The 3rd prize = (a – 20) – 20 = a – 40 And so on So, the series will be a, a – 20, a – 40, …. Since difference is same, it is an AP Here, a = a d = (a – 20) – a = a – 20 – a = –20 Also, Sum of Rs 700 is given, So, Sn = 700 We know that Sn = 𝒏/𝟐 (𝟐𝒂+(𝒏−𝟏)𝒅) Putting a = a, d = −20, Sn = 700 700 = 7/2 (2𝑎+(7−1)×−20) 700 = 7/2 (2𝑎+6 × −20) 700 = 7/2 (2𝑎−120) 700 × 2/7=2𝑎−120 200 = 2a – 120 200 + 120 = 2a 320 = 2a 320/2=𝑎 160 = a a = 160 So, 1st prize = a = Rs 160 2nd prize = a – 20 3rd prize = a – 40 4th prize = a – 60 5th prize = a – 80 6th prize = a – 100 7th prize = a – 120

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.