Question 361 markSection E

How many subscribers will discontinue after an increase of Rs x in annual fee?

Application of Derivatives
Application of Derivatives — Setting up a Revenue Function

Official answer

Since 10 subscribers discontinue for every Rs 1 increase in fee, an increase of Rs x causes 10x10x subscribers to discontinue.

Answer keywords:rate of changelinear relationshipsubscribers discontinuingrevenue modelling

Marking scheme

  1. 1.1 mark: correct expression 10x10x for the number of subscribers who discontinue.

Hint

Multiply the rate (10 subscribers per Rs 1 increase) by the increase amount x.

Quick oral answer

Since 10 subscribers leave for every Rs 1 increase, a Rs x increase causes 10x10x subscribers to discontinue.

Common mistakes

  1. 1.Writing the relationship as x/10x/10 or 10/x10/x instead of the correct 10x10x.
  2. 2.Ignoring units and forgetting x itself represents the rupee increase, not a subscriber count.

Analysis and explanation

This is the first, foundational step of the case study — translating a verbal rate ("10 subscribers discontinue per Rs 1 increase") into an algebraic expression in x.


Concept

  • The relationship is directly proportional: rate of discontinuation × increase amount = 10×x=10x10 \times x = 10x.

Exam trap

  • A common error is writing 10/x10/x or x/10x/10 instead of the correct product 10x10x, confusing the rate with a ratio.

Interesting facts

This kind of 'linear demand response' model (demand falls linearly with price rise) is the simplest and most widely used model in introductory microeconomics and revenue optimisation.

Subscription businesses (OTT platforms, delivery apps) use exactly this kind of price-elasticity modelling in real pricing strategy decisions.

Question details

Q36 of 44 questions

Board
CBSE
Class
Class 12
Subject
Mathematics
Year
2026
Section
Section E
Marks
1
Chapter
Application of Derivatives
Topic
Application of Derivatives — Setting up a Revenue Function
Bloom's level
understand
Syllabus topic
Unit 6: Application of Derivatives — Maxima and Minima (Case Study: Modelling Revenue as a Function of Price Increase)
Author
CBSE
Reviewed by
Padhantu Academic Team

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Frequently asked questions

Why is the relationship 10x10x and not x/10x/10?

Because the rate given is 10 subscribers per Rs 1, so for an increase of x rupees, the total number who leave is 10 multiplied by x, i.e., 10x10x.