Pareto Academy
Log inStart free
CAT QuanteasyArithmetic

Arithmetic I: Percentages, Profit and Interest

Updated 22 October 2026

Five questions on percentages, profit and loss, and simple and compound interest.

Question 1 · Multiple choice (+3 / −1)

A retailer marks a jacket 40% above its cost price and then allows two successive discounts of 10% and 5% on the marked price. What is the retailer's profit percentage?

Show the solution

Answer: B. 19.7%

  1. Take the cost price as ₹100. The marked price is ₹140.
  2. After the 10% discount: 140 × 0.9 = ₹126.
  3. After the further 5% discount: 126 × 0.95 = ₹119.70.
  4. Profit = 119.70 − 100 = ₹19.70 on a cost of ₹100, so the profit is 19.7%.
  5. Shortcut: multiply the factors directly, 1.4 × 0.9 × 0.95 = 1.197. Adding and subtracting the percentages (40 − 10 − 5 = 25%) is the classic trap; successive changes multiply.
Question 2 · Type in the answer (+3 / 0)

On a certain sum lent for 3 years at 10% per annum, the compound interest (compounded annually) exceeds the simple interest by ₹1,240. What is the sum? Enter the answer in rupees.

Show the solution

Answer: 40000

  1. Let the sum be P. Simple interest for 3 years = P × 0.10 × 3 = 0.3P.
  2. Compound interest for 3 years = P(1.1³ − 1) = P(1.331 − 1) = 0.331P.
  3. Difference = 0.331P − 0.3P = 0.031P = 1,240.
  4. P = 1,240 ÷ 0.031 = ₹40,000.
  5. Shortcut: for 3 years, CI − SI = P × r²(3 + r) with r as a decimal: 0.01 × 3.1 = 0.031.
Question 3 · Multiple choice (+3 / −1)

Asha's salary is 25% more than Kabir's. Kabir then gets a 20% raise and Asha a 10% raise. By what percentage does Asha's new salary exceed Kabir's new salary?

Show the solution

Answer: C. 14 7/12%

  1. Let Kabir's salary be 100, so Asha's is 125.
  2. Kabir's new salary = 100 × 1.2 = 120. Asha's new salary = 125 × 1.1 = 137.5.
  3. Excess = 137.5 − 120 = 17.5.
  4. As a percentage of Kabir's new salary: 17.5 ÷ 120 × 100 = 175/12 = 14 7/12%.
  5. Taking the gap as 25 − (20 − 10) = 15% or 25 − 20 + 10 mixes up the bases; always compute both new values.
Question 4 · Type in the answer (+3 / 0)

Meera splits ₹50,000 between two schemes. Scheme A pays simple interest at 10% per annum; scheme B pays compound interest at 20% per annum, compounded annually. After 2 years the total interest from both schemes is ₹15,400. How much did Meera put into scheme A? Enter the answer in rupees.

Show the solution

Answer: 27500

  1. Let ₹x go into scheme A and ₹(50,000 − x) into scheme B.
  2. Scheme A interest in 2 years = x × 0.10 × 2 = 0.2x.
  3. Scheme B interest in 2 years = (50,000 − x)(1.2² − 1) = 0.44(50,000 − x) = 22,000 − 0.44x.
  4. Total: 0.2x + 22,000 − 0.44x = 15,400, so 0.24x = 6,600 and x = 27,500.
  5. Check: A earns ₹5,500 and B (₹22,500) earns ₹9,900; together ₹15,400.
Question 5 · Multiple choice (+3 / −1)

A dishonest trader uses a weight that reads 1 kg but actually weighs 800 g when selling, and sells at a price 10% below the cost price. What is the trader's actual profit percentage?

Show the solution

Answer: C. 12.5%

  1. Let the cost be ₹1 per gram, so 1 kg costs ₹1,000.
  2. The customer pays for 1 kg at 10% below cost: 1,000 × 0.9 = ₹900.
  3. The trader actually hands over only 800 g, which cost ₹800.
  4. Profit = 900 − 800 = ₹100 on a cost of ₹800, so the profit is 100 ÷ 800 = 12.5%.
  5. Shortcut: (selling factor ÷ weight factor) − 1 = 0.9 ÷ 0.8 − 1 = 12.5%.

Full worked solution

  1. Successive percentage changes multiply: a change of a% followed by b% gives a factor of (1 + a/100)(1 + b/100).
  2. Profit % is always measured on the actual cost; with false weights, compare the money received with the cost of the goods actually handed over.
  3. Simple interest = P × r × t. Compound interest = P[(1 + r)ⁿ − 1].
  4. CI − SI at rate r: P × r² for 2 years and P × r²(3 + r) for 3 years.
  5. When a sum is split between two schemes, write one share as x and the other as (total − x), then equate total interest.