Profit, Loss, Discounts and Interest Practice Questions for CAT: 283+ Solved Questions with Step-by-Step Solutions

Solve 283+ Profit, Loss, Discounts and Interest practice questions for CAT with answers and detailed solutions. Free sample questions below.

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.

Profit, Loss, Discounts and Interest: Solved Questions with Step-by-Step Explanations (5 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.

Question 3 · Quantitative Ability MCQ

The compound interest earned on a sum during the first year at a certain annual rate compounded annually is ₹2,000. If the rate of interest is 10% p.a., what is the total compound interest earned over 3 years?

A.
₹6,000
B.
₹6,620
C.
₹6,200
D.
₹6,820

Correct Answer:

Step-by-Step Solution

Key idea: This is a "first-year CI interest reveals the principal" question. Recognise it because in the first year, compound interest equals simple interest (since there is no prior interest to compound on). This gives us the principal directly.

Step 1: Find the principal from year-1 interest.

Year 1 CI interest = $P \times r = P \times 0.10 = 2000$ .

$P = \frac{2000}{0.10} = 20000$

Step 2: Compute year-2 interest.

Year 2 interest is calculated on the amount at end of year 1:

$Amount after year 1 = 20000 \times 1.10 = 22000$

$I_{2} = 22000 \times 0.10 = 2200$

Step 3: Compute year-3 interest.

$Amount after year 2 = 22000 \times 1.10 = 24200$

$I_{3} = 24200 \times 0.10 = 2420$

Step 4: Total compound interest over 3 years.

$Total CI = 2000 + 2200 + 2420 = 6620$

Answer: ₹6,620 (Option B).

Trap: A common error is to compute $3 \times 2000 = 6000$ (treating all years as if they earn the same interest). Under CI, each year's interest grows because the base grows.

Question 4 · Quantitative Ability MCQ

According to standard problem-solving checklists, what is the most efficient first step when a profit and loss question provides only percentage values (like profit % and discount %) but no absolute currency amounts?

A.
Assume Selling Price is 100
B.
Assume Cost Price is 100
C.
Assume Marked Price is 100
D.
Set up a system of linear equations with variables x and y

Correct Answer:

Step-by-Step Solution

Key idea: This tests the standard heuristic for handling missing absolute values in percentage-based problems.

Step 1: Recognise the missing information.

When only percentages are given, the actual scale of the transaction doesn't matter for finding relative answers.

Step 2: Apply the '100 Method'.

Assuming the base value (Cost Price) is 100 turns all subsequent percentage calculations into simple additions or subtractions, avoiding complex fractions.

Answer: Assume Cost Price is 100

Question 5 · Quantitative Ability MCQ

If an article is sold at a loss of $L %$ , which of the following formulas correctly gives the Selling Price ( $S P$ ) in terms of Cost Price ( $C P$ )?

A.
$S P = C P \div (1 - \frac{L}{100})$
B.
$S P = C P \times \frac{L}{100}$
C.
$S P = C P \times (1 - \frac{L}{100})$
D.
$S P = C P \times (1 + \frac{L}{100})$

Correct Answer:

Step-by-Step Solution

Key idea: This tests the standard multiplier formula for calculating Selling Price when a loss percentage is given.

Step 1: Understand what a loss of $L %$ means.

It means the Selling Price is $L %$ less than the Cost Price.

Step 2: Translate this into a mathematical multiplier.

$S P = C P - L % of C P$

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

$S P = C P \times (1 - \frac{L}{100})$

Answer: $S P = C P \times (1 - \frac{L}{100})$

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?

Question 3

The compound interest earned on a sum during the first year at a certain annual rate compounded annually is ₹2,000. If the rate of interest is 10% p.a., what is the total compound interest earned over 3 years?

Question 4

According to standard problem-solving checklists, what is the most efficient first step when a profit and loss question provides only percentage values (like profit % and discount %) but no absolute currency amounts?

Question 5

If an article is sold at a loss of L %, which of the following formulas correctly gives the Selling Price (S P) in terms of Cost Price (C P)?

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Profit, Loss, Discounts and Interest Practice Questions for CAT: 283+ Solved Questions with Step-by-Step Solutions

Chapter Roadmap: Profit, Loss, Discounts and Interest

Profit, Loss, Discounts and Interest

🧾 Profit, Loss and Marked Price

🏷️ Discounts, Pricing and Trade Schemes

📈 Simple and Compound Interest

🤝 Investment, Returns and Business Shares

Topic Hero: Profit, Loss and Marked Price

Profit, Loss and Marked Price

Profit, Loss, Discounts and Interest: Solved Questions with Step-by-Step Explanations (5 Problems)

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

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