SSC CGL Maths Arithmetic Profit and Loss

SSC CGL Maths Arithmetic Profit and Loss is one of the most important topics in the Quantitative Aptitude section. Questions from this chapter are common in SSC CGL, SSC CHSL, Railway, Banking, and other competitive exams. The topic may look simple, but questions can be framed in many different ways using cost price, selling price, marked price, discount, profit percentage, loss percentage, quantity, and false weights.

To score well in this topic, candidates must understand the basic terms first. Once the core concepts are clear, even lengthy-looking questions can be solved quickly using ratios, percentage conversion, and shortcut methods. Profit and Loss is also connected with percentage, ratio, and average, so regular practice is necessary.

What is Profit and Loss?

Profit and Loss is based on buying and selling. When an item is sold at a price higher than its cost price, there is a profit. When it is sold at a price lower than its cost price, there is a loss. The most important terms in Profit and Loss are: 

• Cost Price (CP): The price at which an article is bought.

• Selling Price (SP): The price at which an article is sold.

• Profit: When SP is greater than CP.

• Loss: When CP is greater than SP.

• Marked Price (MP or MRP): The listed price of an article.

• Discount: Reduction given on the marked price.

Students should remember that profit percentage and loss percentage are always calculated on the cost price. This is one of the most important rules in SSC CGL Profit and Loss questions.

Basic Profit and Loss Formulas

Before solving advanced questions, candidates should revise the basic formulas. These formulas are used in almost every question.

Important formulas are:

• Profit = Selling Price − Cost Price

• Loss = Cost Price − Selling Price

• Profit Percentage = Profit / Cost Price × 100

• Loss Percentage = Loss / Cost Price × 100

• Selling Price = Cost Price × (100 + Profit%) / 100

• Selling Price = Cost Price × (100 − Loss%) / 100

• Discount = Marked Price − Selling Price

• Selling Price = Marked Price × (100 − Discount%) / 100

These formulas help students solve direct as well as application-based questions.

Profit and Loss Percentage Calculation

In SSC CGL, many questions ask candidates to calculate the actual profit or loss percentage. For example, if an article is bought for ₹5 and sold for ₹6, the profit is ₹1. Since profit percentage is calculated on the cost price, the profit percentage will be 1/5 × 100 = 20%.

Similarly, if an article is bought for ₹4 and sold for ₹3, the loss is ₹1. The loss percentage will be 1/4 × 100 = 25%.

The main point to remember is:

• Profit or loss percentage is always based on CP.

• Discount percentage is always based on MRP.

• Do not calculate profit or loss percentage on SP unless the question specifically mentions it.

MRP, Discount and Selling Price

Many SSC CGL Maths Profit and Loss questions include the marked price and discount. In such questions, students must understand the relationship between MRP, discount, and selling price.

If an article has an MRP of ₹1000 and a 10% discount is given, the selling price becomes:

₹1000 × 90/100 = ₹900

So, the basic relation is:

Selling Price = MRP − Discount on MRP

A very useful formula for questions involving cost price, marked price, discount, and profit is:

CP / MRP = (100 − Discount%) / (100 + Profit%)

If there is a loss, use loss in the denominator as:

CP / MRP = (100 − Discount%) / (100 − Loss%)

For example, if a shopkeeper earns 12% profit after giving 10% discount, then:

CP / MRP = 90 / 112 = 45 / 56

So, CP : MRP = 45 : 56.

Quantity-Based Profit and Loss Questions

Quantity-based questions are very common in SSC CGL. These questions may involve oranges, lemons, toffees, cloth, or other items bought and sold at different rates. The best method is to equalise the quantity using LCM.

For example, if a person buys 11 lemons for ₹10 and sells 10 lemons for ₹11, equalise the quantity.

LCM of 11 and 10 = 110

• CP of 110 lemons = ₹100

• SP of 110 lemons = ₹121

• Profit = ₹21

• Profit percentage = 21%

This method is simple and avoids confusion in quantity-based questions.

Dishonest Dealer and False Weight Questions

Dishonest dealer questions are also important in SSC CGL Profit and Loss. These questions usually involve false weights or wrong measurements. The shopkeeper may claim to sell at the cost price but give less quantity.

For example, if a dealer uses 850 grams instead of 1 kg, then:

• Cheated quantity = 1000 − 850 = 150 grams

• Actual quantity given = 850 grams

• Profit percentage = 150 / 850 × 100 = 17 11/17%

Another common case is when a dealer gives 80 cm instead of 1 metre. In that case:

• Cheated quantity = 20 cm

• Actual quantity given = 80 cm

• Profit percentage = 20 / 80 × 100 = 25%

Students should practise these questions regularly because they can be solved quickly with the right approach.

Successive Discounts and Marked Price Questions

Successive discount questions are also asked in SSC CGL. If two discounts are given one after another, they should not be directly added. The second discount is always applied after the first discount. For example, if the MRP is ₹720 and the article is sold for ₹550.80 after two discounts, where the first discount is 10%, then:

• Price after first discount = ₹720 × 90/100 = ₹648

• Second discount amount = ₹648 − ₹550.80 = ₹97.20

• Second discount percentage = 97.20 / 648 × 100 = 15%

Such questions require careful calculation and understanding of successive percentage changes.

Important Profit and Loss Tricks for SSC CGL

Candidates can save time by remembering some common tricks.

Useful tricks include:

• If loss at one SP equals profit at another SP, then CP = (SP1 + SP2) / 2.

• If an item is sold at the same SP with equal profit and loss percentages, there is always an overall loss.

• In false weight questions, profit percentage = cheated quantity / actual quantity given × 100.

• Profit and loss percentage must always be calculated on CP.

• Discount is always calculated on the marked price.

• In chain transactions, multiply the successive profit or loss factors.

These tricks help solve questions faster in the exam.

How to Prepare Profit and Loss for SSC CGL?

Profit and Loss can become a scoring topic if students practise it in a proper way. Some preparation tips include:

• Learn all basic formulas first.

• Practise percentage-to-fraction conversion.

• Solve questions based on CP, SP, MP, and discount.

• Practice dishonest dealer and false weight questions.

• Solve quantity-based questions using LCM.

• Revise successive discount questions.

• Attempt SSC CGL previous year questions.

• Avoid calculation mistakes in percentage-based problems.