Profit, Loss, Discounts and Interest Notes for CAT: Concepts, Formulas, Worked Examples & Practice

Profit, Loss, Discounts and Interest notes for CAT: 96 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

Chapter Roadmap: Profit, Loss, Discounts and Interest

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Chapter Journey

Profit, Loss, Discounts and Interest

Step 1 • 9 CAT PYQs • Importance 0.57

🧾 Profit, Loss and Marked Price

Master CP, SP, MP, profit %, loss %, same-selling-price puzzles, overheads, and transaction chains.

Step 2 • 6 CAT PYQs • Importance 0.45

🏷️ Discounts, Pricing and Trade Schemes

Handle successive discounts, offers, bundles, and hidden pricing logic.

Step 3 • 10 CAT PYQs • Importance 0.62

📈 Simple and Compound Interest

Move from basic interest to compounding, installments, and rate-time traps.

Step 4 • 5 CAT PYQs • Importance 0.41

🤝 Investment, Returns and Business Shares

Use ratios, weighted returns, and partnership logic to split gains fairly.

By the end of this chapter: you should be able to convert every money question into a clean equation of cost, selling value, profit, loss, or return.

Topic Hero: Profit, Loss and Marked Price

CAT Quant • Arithmetic

Profit, Loss and Marked Price

The art of tracking money: what you paid, what you tagged, what you received, and what you gained or lost.

Cost Price

Marked Price

Selling Price

Core CAT skill: choose the correct base. Profit and loss are usually on CP. Discount is usually on MP. Rupee profit is SP minus CP.

The Money Flow: CP → MP → SP

The basic money chain

Profit

When $S P > C P$

Profit $= S P - C P$

Loss

When $S P < C P$

Loss $= C P - S P$

Profit % and Loss %: Always Ask ‘Percent of What?’

The two master formulas

Profit percentage

$Profit % = \frac{S P - C P}{C P} \times 100$

Loss percentage

$Loss % = \frac{C P - S P}{C P} \times 100$

Multiplier form:

Profit of $p %$ : $S P = C P (1 + \frac{p}{100})$

Loss of $l %$ : $S P = C P (1 - \frac{l}{100})$

Profit, Loss, Discounts and Interest: Solved Questions with Step-by-Step Explanations (2 Problems)

Question 1 · Quantitative Ability MCQ

If a sum of money "doubles" in 5 years under simple interest, what does the total interest earned over those 5 years strictly equal in terms of the original principal $P$ ?

A.
$2 P$
B.
$0.5 P$
C.
$P$
D.
$5 P$

Correct Answer:

Step-by-Step Solution

Key idea: This is a "doubling/tripling" terminology question, recognisable by words like "doubles", "triples", or "becomes three times".

Step 1: "Doubles" means the final Amount $A$ is equal to $2 P$ .

Step 2: Recall the fundamental relationship: $Amount = Principal + Interest$ .

Step 3: Substitute the knowns: $2 P = P + Interest$ .

Step 4: Solve for Interest: $Interest = 2 P - P = P$ .

Answer: $P$ .

Question 2 · Quantitative Ability MCQ

A bank offers 12% per annum interest, compounded annually. A customer deposits ₹10,000 and withdraws all credited interest at the end of each year, leaving only the original principal in the account. What is the total interest received by the customer over 3 years?

A.
₹4,049
B.
₹3,600
C.
₹3,972
D.
₹3,648

Correct Answer:

Step-by-Step Solution

Key idea: This is a "compounding neutralised by withdrawal" question. Recognise it because the scheme says "compounded annually" BUT the customer withdraws interest each year, preventing it from being reinvested.

Step 1: Identify what happens when interest is withdrawn.

The bank credits interest at the end of each year. But the customer immediately withdraws it. So the interest never sits in the account to earn further interest. The principal remains ₹10,000 throughout.

Step 2: Determine effective interest type.

Since the base never changes (always ₹10,000), each year's interest is:

$10000 \times \frac{12}{100} = ₹1, 200$

This is identical every year — the definition of simple interest.

Step 3: Calculate total over 3 years.

$Total interest = 1200 \times 3 = ₹3, 600$

Answer: ₹3,600 (Option B).

Trap: The word "compounded annually" is a distractor. Compounding only matters if interest stays in the account. Since it is withdrawn, the effective behaviour is simple interest. Computing $10000 (1.1 2^{3} - 1) = ₹4, 049$ would be wrong because that assumes interest is reinvested.

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Profit, Loss, Discounts and Interest Notes for CAT: Concepts, Formulas, Worked Examples & Practice

Profit, Loss, Discounts and Interest notes for CAT: 96 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

A question from this chapter

Question 1

If a sum of money "doubles" in 5 years under simple interest, what does the total interest earned over those 5 years strictly equal in terms of the original principal P ?

Question 2

A bank offers 12% per annum interest, compounded annually. A customer deposits ₹10,000 and withdraws all credited interest at the end of each year, leaving only the original principal in the account. What is the total interest received by the customer over 3 years?

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