Profit and Loss for SSC & Railway Exams: Formulas, Tricks, Examples and Practice Questions
Profit and Loss is one of the most important arithmetic chapters for competitive examinations such as SSC CGL, SSC CHSL, SSC MTS, SSC GD, RRB NTPC and Railway Group D.
The chapter is closely connected with percentage. Therefore, students should understand basic percentage concepts before starting Profit and Loss.
Questions may involve cost price, selling price, profit percentage, loss percentage, marked price, discount and dishonest shopkeepers.
Basic Terms in Profit and Loss
Cost Price
The price at which an article is purchased is called its Cost Price (CP).
Selling Price
The price at which an article is sold is called its Selling Price (SP).
Profit
If the selling price is greater than the cost price, there is a profit.
Profit = SP - CP
Loss
If the cost price is greater than the selling price, there is a loss.
Loss = CP - SP
Profit Percentage
Profit Percentage = (Profit / Cost Price) × 100
Example
An article is purchased for ₹500 and sold for ₹600.
Profit = 600 - 500 = ₹100
Profit% = (100/500) × 100
= 20%
Answer: 20%
Loss Percentage
Loss Percentage = (Loss / Cost Price) × 100
Example
An article is purchased for ₹800 and sold for ₹680.
Loss = 800 - 680 = ₹120
Loss% = (120/800) × 100
= 15%
Answer: 15%
Finding Selling Price When Profit Percentage is Given
SP = CP × (100 + Profit%)/100
Example
An article costing ₹1,200 is sold at a profit of 25%.
SP = 1200 × 125/100
= ₹1,500
Answer: ₹1,500
Finding Selling Price When Loss Percentage is Given
SP = CP × (100 - Loss%)/100
Example
An article costing ₹2,000 is sold at a loss of 15%.
SP = 2000 × 85/100
= ₹1,700
Answer: ₹1,700
Finding Cost Price from Selling Price
If an article is sold at x% profit:
CP = SP × 100/(100 + x)
Example
An article is sold for ₹1,440 at a profit of 20%.
CP = 1440 × 100/120
= ₹1,200
Answer: ₹1,200
If an article is sold at x% loss:
CP = SP × 100/(100 - x)
Important Point: Profit and Loss are Usually Calculated on Cost Price
A common mistake is to calculate profit percentage using selling price.
Unless the question explicitly says otherwise:
Profit% and Loss% are calculated on Cost Price.
Marked Price and Discount
The price written or printed on an article is called its Marked Price (MP).
Discount = Marked Price - Selling Price
Discount Percentage = (Discount / Marked Price) × 100
Example
The marked price of a shirt is ₹2,000. A discount of 15% is offered.
Discount = 15% of 2000
= ₹300
Selling Price = 2000 - 300
= ₹1,700
Answer: ₹1,700
Successive Discounts
If two successive discounts are a% and b%, equivalent discount is:
a + b - (ab/100)
Example
A shopkeeper gives successive discounts of 20% and 10%.
Equivalent discount:
20 + 10 - (20 × 10)/100
= 30 - 2
= 28%
Answer: 28%
Profit After Discount
Questions frequently combine marked price, discount and profit.
Example
A shopkeeper marks an article 25% above its cost price and gives a discount of 10%.
Assume CP = ₹100.
Marked Price = ₹125
Selling Price after 10% discount:
125 × 90/100 = ₹112.50
Profit = ₹12.50
Profit% = 12.5%
Answer: 12.5% profit
Selling Two Articles at Same Selling Price
This is an important competitive-exam concept.
Suppose two articles are sold at the same selling price, one at x% profit and the other at x% loss.
There is always an overall loss.
Overall Loss% = x²/100
Example
Two articles are sold for the same selling price. One is sold at 20% profit and the other at 20% loss.
Overall loss:
20²/100 = 4%
Answer: 4% loss
False Weight and Dishonest Shopkeeper
A dishonest shopkeeper may claim to sell goods at cost price but use less weight.
Example
A shopkeeper claims to sell 1 kg for the cost price of 1 kg but actually gives only 800 g.
Suppose the cost of 1 kg = ₹100.
Cost of 800 g = ₹80.
Selling price = ₹100.
Profit = ₹20.
Profit% = (20/80) × 100
= 25%
Answer: 25% profit
Important Shortcuts
If profit is x%:
SP : CP = (100 + x) : 100
If loss is x%:
SP : CP = (100 - x) : 100
For 20% profit:
SP : CP = 120 : 100 = 6 : 5
For 25% profit:
SP : CP = 125 : 100 = 5 : 4
For 20% loss:
SP : CP = 80 : 100 = 4 : 5
These ratios can make calculations much faster.
Common Mistakes
1. Taking Selling Price as the Base
Profit percentage is generally calculated on cost price.
2. Adding Successive Discounts
20% and 10% successive discounts are not equal to 30%.
Their equivalent discount is 28%.
3. Confusing Marked Price and Cost Price
Marked Price is not necessarily the purchase price of the shopkeeper.
4. Assuming Equal Profit and Loss Cancel
Selling two items at equal selling price with equal profit and loss percentages results in an overall loss.
Practice Questions
An article is purchased for ₹800 and sold for ₹920. Find the profit percentage.
An article costing ₹1,500 is sold at a loss of 12%. Find its selling price.
An article is sold for ₹1,320 at a profit of 10%. Find its cost price.
A shirt marked at ₹2,400 is sold at a discount of 15%. Find the selling price.
Find the equivalent discount of successive discounts of 20% and 15%.
A shopkeeper marks an article 40% above cost price and gives a discount of 20%. Find the profit percentage.
Two articles are sold at the same price, one at 10% profit and another at 10% loss. Find the overall loss percentage.
A shopkeeper uses 900 g instead of 1 kg but charges the cost price of 1 kg. Find the profit percentage.
An article is sold for ₹2,250 at a loss of 10%. Find the cost price.
If CP : SP = 5 : 6, find the profit percentage.
Answers
15%
₹1,320
₹1,200
₹2,040
32%
12% profit
1% loss
11⅑% profit
₹2,500
20%
Frequently Asked Questions
What is the most important formula in Profit and Loss?
Profit% = Profit/CP × 100 and Loss% = Loss/CP × 100 are the basic formulas.
Is Profit and Loss important for SSC exams?
Yes. It is a major arithmetic topic and is also closely connected with percentage and discount.
What should I study before Profit and Loss?
Students should understand percentage, fractions and ratios.
What should I study after Profit and Loss?
Discount, Simple Interest and Compound Interest are good next topics.
Conclusion
Profit and Loss becomes much easier when students understand the relationship between Cost Price, Selling Price and Percentage.
Instead of memorising too many tricks, first master basic formulas and then practise mixed questions involving discount, marked price, successive discount and dishonest shopkeepers.
Regular practice is essential for increasing both speed and accuracy in SSC and Railway examinations.