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

Profit, Loss, Discounts and Interest short notes for CAT: 28 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

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

The Base Trap: Profit on CP, Discount on MP

One topic, two different bases

Phrase in question	Base	Meaning
Profit of $20%$	CP	$S P = 1.20 C P$
Loss of $10%$	CP	$S P = 0.90 C P$
Discount of $10%$	MP	$S P = 0.90 M P$

CAT warning: whenever a question has both marked price and profit, write the chain:

C P \to M P \to S P

Which Equation Should You Write?

Pattern → best first move

Question signal	Best first move
Cost changed by a percentage	Let old CP be $C$ ; write old SP and changed SP.
Two objects sold at same price	Let common SP be $S$ .
Wage, rent, employee, transport	Use net profit $=$ revenue $-$ all costs.
Free quantity or short measure	Find effective CP and SP per actual unit.

Common CAT Traps in Profit and Loss

Do not fall for these

Trap 1: Treating MP as SP. MP is only the tag.

Trap 2: Calculating profit percentage on SP. Profit/loss percent is usually on CP.

Trap 3: Ignoring wage or overhead. Net profit means all costs are included.

Trap 4: Comparing ₹ per billed unit with ₹ per actual unit. Normalize quantity first.

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 Short Notes for CAT: Concepts, Formulas, Worked Examples & Practice

Profit, Loss, Discounts and Interest short notes for CAT: 28 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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