RRB Group D Maths Profit and Loss: Formulas, Key Terms, and Solved Examples

Profit and Loss is an important topic in the Mathematics section of the Railway Recruitment Board RRB Group D examination. Many questions in the exam are based on simple concepts of buying and selling. If a student understands the basic ideas and formulas, solving these questions becomes easier. Regular practice and clarity of concepts can help aspirants solve these questions quickly during the exam.

This topic mainly focuses on three basic ideas: Cost Price, Selling Price, and the difference between them. Questions are usually asked on profit percentage, loss percentage, ratio problems, and situations where additional expenses or dishonest practices affect the final result. Understanding these ideas step by step helps in solving both simple and slightly advanced questions.

Basic Terms to Remember in Profit and Loss

To solve these problems, you must know four main terms:

• Cost Price (CP): This is the price at which you buy an item.

• Selling Price (SP): This is the price at which you sell an item.

• Profit: You make a profit if the Selling Price is more than the Cost Price (SP > CP).

• Loss: You face a loss if the Cost Price is more than the Selling Price (CP > SP).

Also Read:

• RRB Group D Maths Compound Interest
• RRB Group D Maths Ratio and Proportion

Important Formulas of Profit and Loss

In the exam, you will often need to calculate the percentage of profit or loss. Always remember that Profit % and Loss % are calculated on the Cost Price (CP).

1. Profit Percentage:
   

2. Loss Percentage:
   

3. Finding CP when SP and Profit/Loss % are given:
   

Common Problem Types in RRB Group D

1. Additional Expenses

Sometimes, a person buys an old item and spends money on repairs. In this case, the Total Cost Price is the purchase price plus the repair cost.

• Example: If you buy a phone for ₹1200 and spend ₹200 on repairs, your total CP is ₹1400.

2. Ratio Problems

The exam may give the ratio of CP and SP.

• Example: If the ratio of CP to SP is 20:21, the profit is 1 unit. You can then find the percentage using the CP of 20 units.

3. Dishonest Dealer Problems

Some shopkeepers use less weight to make more profit.

Problem: A shopkeeper sells his goods at a 20% profit. In addition, he uses a weight of 600 grams instead of 800 grams. Calculate his overall profit percentage.

Solution Method: Combining Ratios of Price and Weight

(Memory Tip: Represent both weight and price manipulation as ratios, then multiply them to find the overall effect.)

1. Weight Manipulation Ratio (CP:SP from weight):

• For 600 grams given, he charges for 800 grams.

• Ratio of CP (actual weight) : SP (charged weight) = 600 : 800 = 3 : 4.

2. Profit Declaration Ratio (CP:SP from declared profit):

• Sells at 20% profit. 20% = 1/5.

• If CP = 5 units, Profit = 1 unit, then SP = 6 units.

• Ratio CP : SP = 5 : 6.

3. Combine Ratios (Overall CP : SP):

• Overall CP = (Weight CP) × (Declared CP) = 3 × 5 = 15.

• Overall SP = (Weight SP) × (Declared SP) = 4 × 6 = 24.

• Combined CP : SP is 15 : 24.

4. Overall Profit Percentage:

• Profit = 24 - 15 = 9 units.

• Profit Percentage = (Profit / CP) × 100 = (9 / 15) × 100 = (3 / 5) × 100 = 60%.

4. When Profit Equals Loss

Problem: The profit earned by selling an article for ₹625 is the same as the loss incurred by selling the same article for ₹435. Find the Cost Price (CP) of the article.

Solution Method:

(Memory Tip: When the profit amount from one selling price is equal to the loss amount from another selling price for the same article, the Cost Price (CP) is the average of the two selling prices.)

1. CP = (Selling Price 1 + Selling Price 2) / 2

2. CP = (₹625 + ₹435) / 2 = ₹1060 / 2 = ₹530.

Examples of Profit and Loss

Example 1: The ratio of the Cost Price (CP) to the Selling Price (SP) of an inkpot is 20:21. Calculate the Profit Percentage.

Solution:

1. Given CP = ₹20, SP = ₹21.

2. Profit = SP - CP = ₹21 - ₹20 = ₹1.

3. Profit % = (Profit / CP) × 100 = (₹1 / ₹20) × 100 = 5%.

Example 2: If the Selling Price (SP) of an elephant is 8/5 times its Cost Price (CP), find the Profit Percentage.

Solution:

1. "8/5 times its Cost Price (CP)" means CP = 5 units, SP = 8 units.

2. Profit = SP - CP = 8 - 5 = 3 units.

3. Profit % = (Profit / CP) × 100 = (3 / 5) × 100 = 60%.

Example 3: If a book is sold for ₹270, resulting in a 10% loss, find the Cost Price (CP).

Solution Method 1: Using Fractions

1. 10% Loss = 1/10. Denominator (10) is CP, numerator (1) is Loss.

2. CP = 10 units, Loss = 1 unit, so SP = CP - Loss = 9 units.

3. Given SP = ₹270. So, 9 units = ₹270, which means 1 unit = ₹30.

4. CP = 10 units = 10 × ₹30 = ₹300.

Solution Method 2: Using Formulas

• To find CP (when buying), use CP = SP × 100 / (100 ± Profit/Loss %). (Memory Tip: When finding CP, '100' is in the numerator.)

• To find SP (when selling), use SP = CP × (100 ± Profit/Loss %) / 100. (Memory Tip: When finding SP, '100' is in the denominator.)

1. Given SP = ₹270 and Loss = 10%.

2. CP = ₹270 × 100 / (100 - 10) = ₹270 × 100 / 90 = ₹300.

Example 4: Atul bought an old mobile for ₹1200 and spent ₹200 on its repair. He sold it for ₹1680. Find his Profit Percentage.

Solution:

1. Total CP = ₹1200 + ₹200 = ₹1400.

2. SP = ₹1680.

3. Profit = SP - Total CP = ₹1680 - ₹1400 = ₹280.

4. Profit % = (Profit / Total CP) × 100 = (₹280 / ₹1400) × 100 = 20%.

Example 5: A profit received on selling an article is 3/8 times of its Selling Price (SP). Find the Profit Percentage.

Solution:

1. "Profit… 3/8 times of its Selling Price (SP)" means SP = 8 units, Profit = 3 units.

2. CP = SP - Profit = 8 - 3 = 5 units.

3. Profit % = (Profit / CP) × 100 = (3 / 5) × 100 = 60%.

Example 6: The Cost Price (CP) of 25 toys is equal to the Selling Price (SP) of 20 toys. Find the Profit Percentage.

Solution:

1. 25 CP = 20 SP.

2. Simplify: 5 CP = 4 SP.

3. Inverse relationship: CP = 4 units, SP = 5 units.

4. Profit = SP - CP = 5 - 4 = 1 unit.

5. Profit % = (Profit / CP) × 100 = (1 / 4) × 100 = 25%.

Profit and Loss is a simple but important topic in the RRB Group D Maths Syllabus. Most questions are based on clear formulas and logical thinking. Students who understand Cost Price, Selling Price, Profit, and Loss can solve many problems without difficulty.

Practice plays an important role in mastering this topic. Solving different types of questions helps students recognize patterns and apply the correct method quickly. Regular revision of formulas also helps during the exam.