An article bought for ₹400 is sold for ₹500. What is the profit percent?

25%. Profit = 500 - 400 = ₹100, so profit percent = 100400 100 = 25\%.

By selling an article for ₹270 a man loses 10%. What is the cost price?

₹300. SP is 90\% of CP, so CP = 2700.9 = ₹300.

A shopkeeper marks an item 40% above its cost and then allows a 25% discount. What is his profit percent?

5%. Take CP = 100: MP = 140 and SP = 140 0.75 = 105. Profit percent = 5\%.

A man sells two watches for ₹1,200 each, gaining 20% on one and losing 20% on the other. What is his overall percentage loss?

4%. Selling two items at the same price with +20\% and -20\% always gives a net loss of 20^2100 = 4\%.

A trader sells goods at cost price but uses a weight of 900 g for a kilogram. What is his profit percent?

11 19\%. He hands over 900 g but charges for 1000 g, gaining 100 g of goods on every 900 g sold. Profit percent = 100900 100 = 11 19\%.

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Quantitative Aptitude · Commercial Maths

Profit and Loss — Questions & Answers

Profit and loss questions revolve around cost price, selling price, marked price and discount. Percentages here are almost always taken on the cost price unless the question says otherwise.

5 solved questions
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Key formulas included

Key formulas

$\text{Profit\%} = \dfrac{SP - CP}{CP}\times 100$ ; $\;\text{Loss\%} = \dfrac{CP - SP}{CP}\times 100$
$SP = CP\left(1 + \dfrac{\text{Profit\%}}{100}\right)$ ; $\;SP = \text{MP}\left(1 - \dfrac{\text{Discount\%}}{100}\right)$
Selling two items at the same price with $+x\%$ and $-x\%$ always gives a net loss of $\dfrac{x^2}{100}\%$

5 solved Profit and Loss questions

Try each question first — tap an option to check your answer, or open Learn step by step for a guided walkthrough.

01
An article bought for ₹400 is sold for ₹500. What is the profit percent?
4 steps · reveal one at a time
1. Step 1: Identify key values
  We need to find the profit percent. The article was bought for ₹400, which is the Cost Price (CP). It was sold for ₹500, which is the Selling Price (SP).
2. Step 2: Calculate the profit
  First, let's find the actual profit made. Profit is the difference between the Selling Price and the Cost Price. So, Profit $= \text{SP} - \text{CP} = \text{\text{Rs}\,}500 - \text{\text{Rs}\,}400 = \text{\text{Rs}\,}100$ .
3. Step 3: Calculate profit percent
  Now, we calculate the profit percent using the formula: Profit Percent $= \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100$ . Plugging in our values, Profit Percent $= \left( \frac{\text{\text{Rs}\,}100}{\text{\text{Rs}\,}400} \right) \times 100 = \frac{1}{4} \times 100 = 25\%$ .
4. Step 4: The answer
  So the answer is (B) 25%. Our calculation shows a profit of 25% when an item bought for ₹400 is sold for ₹500.
02
By selling an article for ₹270 a man loses 10%. What is the cost price?
4 steps · reveal one at a time
1. Step 1: Understand the Loss
  When a man loses 10% by selling an article, it means the Selling Price (SP) is 100% - 10% = 90% of the Cost Price (CP).
2. Step 2: Formulate the Equation
  We are given that the Selling Price is ₹270. So, we can express the relationship as $SP = 0.90 \times CP$ .
3. Step 3: Calculate Cost Price
  Substitute the known SP into the equation: $270 = 0.90 \times CP$ . To find the Cost Price, divide ₹270 by 0.90. This gives $CP = \frac{270}{0.90}$ .
4. Step 4: The answer
  So the answer is (C) ₹300. Performing the division, $CP = 300$ . This means the original cost price of the article was ₹300.
03
A shopkeeper marks an item 40% above its cost and then allows a 25% discount. What is his profit percent?
5 steps · reveal one at a time
1. Step 1: Assume Cost Price
  To simplify calculations, let's assume the Cost Price (CP) of the item is $\$ 100$. This makes it straightforward to work with percentages.
2. Step 2: Find Marked Price
  The shopkeeper marks the item 40% above its cost. So, the Marked Price (MP) will be $100 + 40\% \text{ of } 100 = 100 + 40 = \$ 140$.
3. Step 3: Determine Selling Price
  A 25% discount is allowed on the Marked Price. So, the Selling Price (SP) is $140 \times (1 - 0.25) = 140 \times 0.75 = \$ 105$.
4. Step 4: Calculate Profit Percent
  The profit is $SP - CP = 105 - 100 = \$ 5 $. Since the CP was$ $100 $, the **profit percent** is$ (\text{Profit} / CP) \times 100 = (5 / 100) \times 100 = 5%$.
5. Step 5: The answer
  So the answer is (B) 5%. The final selling price is $\$ 105 $for an item that cost$ $100$, resulting in a 5% profit.
04
A man sells two watches for ₹1,200 each, gaining 20% on one and losing 20% on the other. What is his overall percentage loss?
5 steps · reveal one at a time
1. Step 1: Analyze the Scenario
  A man sells two watches, each for ₹1,200. He gains 20% on one watch and loses 20% on the other. We need to determine his overall percentage loss from these transactions.
2. Step 2: Recognize the Pattern
  This is a common type of problem. When two items are sold at the same price, and there's an equal percentage gain on one and an equal percentage loss on the other, there will always be an overall loss.
3. Step 3: Apply the Formula
  For this specific scenario, the overall percentage loss can be calculated using the formula: $\left( \frac{\text{common percentage}}{10} \right)^2$ . Here, the common percentage is 20%.
4. Step 4: Calculate the Loss
  Using the formula, the overall percentage loss is $\left( \frac{20}{10} \right)^2 = (2)^2 = 4\%$ . The selling price of ₹1,200 per watch is not needed for this calculation.
5. Step 5: The answer
  So the answer is (C) 4%. The man experiences an overall 4% loss when selling two items at the same price with equal percentage gain and loss.
05
A trader sells goods at cost price but uses a weight of 900 g for a kilogram. What is his profit percent?
4 steps · reveal one at a time
1. Step 1: Understand the deception
  The trader sells goods at cost price, but uses a false weight. When a customer asks for 1 kg (1000 g), the trader actually provides only 900 g of goods.
2. Step 2: Calculate the profit in goods
  For every 900 g of goods he gives, he charges for 1000 g. This means he effectively gains $1000 \text{ g} - 900 \text{ g} = 100 \text{ g}$ of goods for every 900 g he sells.
3. Step 3: Calculate profit percentage
  The profit is 100 g on an actual sale of 900 g. So, the profit percentage is calculated as $\frac{\text{Profit}}{\text{Actual Quantity Sold}} \times 100$ . This gives $\frac{100}{900} \times 100$ .
4. Step 4: The answer
  So the answer is (C) $11\tfrac{1}{9}\%$ . Calculating $\frac{100}{900} \times 100 = \frac{1}{9} \times 100 = 11.11...\%$ , which is $11\tfrac{1}{9}\%$ .

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