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 $10x$ subscribers to discontinue.

rate of changelinear relationshipsubscribers discontinuingrevenue modelling

Marking Scheme

11 mark: correct expression $10x$ 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 $10x$ subscribers to discontinue.

Analysis & 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 = $10 \times x = 10x$ .

Exam trap

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

Common Mistakes

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

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.

Spotted a mistake or something unclear?

Tell us — we fix reported answers fast.

Frequently Asked Questions

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

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., $10x$ .