Profit and Loss Questions

Profit and loss questions are crucial in understanding the concept of profit and loss. This concept in mathematics has some actual applications in our daily lives, making it more essential to have a proper understanding of profit and loss. This article presents questions based on profit and loss of different types with detailed explanations and tricks, which will help students escalate their problem-solving skills.

Generally, when we sell a thing higher than the price at which it was bought, we say there is a “profit”. In contrast, when we sell something lower than the price at which it was purchased, it’s a condition of “loss”.

Learn more about Profit and Loss.

Some important formulas for solving profit and loss questions:

Profit and Loss Questions with Solutions

Question 1: By selling 90 ball pens for ₹160 a person loses 20%. How many ball pens should be sold for ₹96 so as to have a profit of 20%?

Solution:

S.P. of 90 ball pens = ₹160

Loss % = 20%

∴ C.P. of 90 ball pens = [100/(100 – Loss%)] × Selling Price = [100/(100 – 20)] × 160

= (100 × 160)/80 = ₹200

C.P. of 1 ball pen = ₹ 20/9

Now we find how many pens should be sold for ₹96 to have a profit of 20%

Let us say, ‘x’ number of pens be sold for ₹96

Then, S.P. of x pens = ₹96

C.P of x pens = ₹(20/9)x

Profit = S.P – C.P. = 96 – 20x/9

Profit% = (Profit/ C.P.) × 100

⇒ x = (96 × 9)/24 = 36

Therefore, 36 pens should be sold for ₹96 for a 20% profit.

Question 2: Arun sells an object to Benny at a profit of 15%, Benny sells that object to Chandan for ₹1012 and makes a profit of 10%. At what cost did Arun purchase the object?

Solution:

Let the actual cost price at which Arun bought the object be x

When Arun sells the object to Benny

Profit % = 15%

∴ selling price of object = [(100 + 15)/100] × x = 1.15x

Now, this cost price of the object for Benny

When Benny sells the object to Chandan

Selling Price = ₹1012

Profit % = 10%

∴ Selling price = [(100 + 10)/100] × 1.15x

⇒ 1012 = [(100 + 10)/100] × 1.15x

= ₹800

Therefore, the price at which Arun bought the object is ₹800.

Question 3: A shopkeeper takes 10% profit on his goods. He lost 20% of his goods during a theft. What is his loss per cent?

Solution:

Let the number of goods be 100, and

C.P. of each item be ₹1

∴ Total C.P. = ₹100

Profit% on each item = 10%

20% of goods are lost in a theft

Number of goods left = 80

Now, S.P. of 1 item = [(100 + 10)/100] × 1 = ₹1.10

S.P. of 80 items = 80 × ₹1.10 = ₹88

Loss = 100 – 88 = 12

Loss% = (12/100) × 100% = 12%

Thus, the shopkeeper bears 12% loss.

Question 4: By selling 100 notebooks, a shopkeeper gains the selling price of 20 notebooks. What is his gain percentage?

Solution:

Let the SP of 1 notebook be ₹1

SP of 100 notebooks = ₹100

Now, gain = selling price of 20 notebooks = ₹20

Then CP = SP – Gain = 100 – 20 = ₹80

Gain% = (20/80) × 100% = 25%

Question 5: A television and a washing machine were sold for ₹12500 each. If the television was sold at a gain of 30% and the washing machine at a loss of 30%. Find the overall profit% or loss% on the entire transaction?

Solution:

Total SP = 2 × 12500 = ₹25000

CP of TV = [100/ (100 + 30)] × 12500 = 12500 × 100/130

CP of Washing machine = [100/ (100 – 30)] × 12500 = 12500 × 100/70

∴ Total CP = 12500 [(100/130) + (100/70)] = ₹ 12500 × 200/91 = ₹2500000/91

Clearly SP < CP, that is, there is a loss.

= (225000/2500000) × 100 = 9%

Therefore, there is loss of 9%

Shortcut Method: Using the above trick, here profit% is equal to loss%, that is P = L

∴ Loss% = P²/100 = 30²/100 = 900/100 = 9%

Question 6: A man sold two steel chairs for ₹ 500. On one, he gains 20% and on the other, he loses 12%. How much does he gain or lose on the whole transaction?

Solution:

Total S.P = 2 × 500 = ₹ 1000

C.P. of one chair = [(500 × 100)/20 + (500 × 100)/80]

= [(1250/3) + (6250/11)] = ₹ 32500/33

∴ Gain = 1000 – 32500/33 = ₹ 500/33

∴ Gain% = (500/33)/(32500/33) = 1.53%

Shortcut Method: Here Profit% = P = 20

Loss% = L = 12

Using the formula, [100(P – L) – 2PL]/[(100 + P) + (100 – L)]

= [800 – 480]/[120 + 88] = 320/208 = 1.53%

Question 7: A dishonest shopkeeper pretends to sell his goods at cost price but uses false weights and gains 11¹/₉%. Find the false weight he is using instead of 1kg weight.

Solution:

Let the false weight be x gm.

Gain % = [(True weight – False weight)/ False weight]×100

⇒ 100/9 = [(1000 – x)/x] × 100

⇒ 10 x = 9000

⇒ x = 900

∴ the shopkeeper is using weights of 900 gm instead of 1kg.

Question 8: Manny bought an AC for ₹ 12160 and paid ₹ 340 for transportation. Then he sold it for ₹12875. Find his profit %.

Solution:

CP of AC = Actual CP + Transportation cost = 12160 + 340 = 12500

SP of AC = ₹ 12875

Profit = 12875 – 12500 = ₹ 375

Profit % = 375/12500 × 100 = 3%

Also Read:

• Simple Interest
• Compoud Interest
• Ratio and Proportion
• Percentage

Question 9: If an article is sold for ₹ 178 at a loss of 11%, what should be its selling price in order to earn a profit of 11%?

Solution:

SP of the article = ₹ 178

Loss % = 11%

∴ CP = {100/(100 – 11)} × 178

= (178 × 100)/89 = ₹ 200

Now CP = ₹ 200 and Profit% = 11%

∴ SP = {(100 + 11)/100} × 200 = (110 × 200)/100 = ₹ 222.

Therefore, the article should be sold at ₹ 222.4

Question 10: A cloth merchant sold half of his coth at 20% profit, half of the remaining at 20% loss and the rest was sold at the cost price. Calculate the overall profit% or loss%?

Solution:

Let the CP of the whole cloth be x

CP of ½ cloth = x/2

CP of half of the remaining = x/4

SP of first half of cloth = (120 × x/2) ÷ 100

SP of the half of the remaining cloth = (80 × x/4) ÷ 100

SP of the remaining half = x/4

= ₹ 21x/20

Gain = 21x/20 – x = ₹ x/20

Related Articles on Maths Questions

• Square Questions
• Geometry Questions
• Surface Area and Volume Questions
• Sequence and Series Questions
• Area Related to Circles Questions

Practice Questions

1. A sold a watch to B at a 20% gain and B sold it to C at a loss of 10%. If C bought the watch for ₹ 216, at what price did A purchase the watch?

2. If 6 articles are sold for ₹ 20 then there is a loss of 20%. In order to gain 20% what must be the number of articles sold for ₹ 20?

3. A dishonest shopkeeper claims to sell his goods at a cost price but uses a weight of 800 gm instead of the standard 1kg weight. What is his profit margin?

4. A dealer uses a scale of 90 cm instead of a metre scale and claims to sell at a cost price. What is his gain%?