Crack SSC CGL & CHSL Quant: Complete Guide to Profit and Loss with Tricks and Solved Questions

Introduction to Profit and Loss for SSC Exams

Welcome, SSC aspirants! If you're gearing up for the SSC CGL or CHSL exams, you know that the Quantitative Aptitude section can be a game-changer. Within this section, 'Profit and Loss' is a topic you simply cannot afford to ignore. It's not just about marks; it's a topic that tests your basic mathematical reasoning, analytical skills, and speed. Questions from Profit and Loss appear consistently every year in both Tier-1 and Tier-2 exams, typically carrying a weightage of 2-4 questions. Mastering this chapter can significantly boost your overall score and bring you closer to your dream government job.

This comprehensive guide is designed to take you from the absolute basics to advanced problem-solving techniques. We will break down every concept, provide you with all the necessary formulas, share time-saving tricks, and walk you through a variety of solved examples. By the end of this post, you'll have the confidence and the skills to tackle any Profit and Loss question thrown at you in the exam hall.

Fundamental Concepts of Profit and Loss

Before we dive into complex problems, let's build a strong foundation. Understanding these core terms is non-negotiable.

Cost Price (CP)

The Cost Price is the price at which an article is purchased. It includes all the overhead expenses like transportation, taxes, and repairs incurred before the item is put up for sale. For example, if a shopkeeper buys a radio for ₹500 and spends ₹50 on its transportation, the total CP for the shopkeeper is ₹550.

Selling Price (SP)

The Selling Price is the price at which an article is sold. This is the amount the customer pays to the seller.

Profit or Gain

When the Selling Price (SP) of an article is greater than its Cost Price (CP), the seller makes a profit or gain.
Profit = Selling Price (SP) – Cost Price (CP)

Loss

When the Selling Price (SP) of an article is less than its Cost Price (CP), the seller incurs a loss.
Loss = Cost Price (CP) – Selling Price (SP)

Marked Price (MP) or List Price

The Marked Price is the price that is marked on the label of an article. It is the price at which the seller intends to sell the product, before applying any discounts. It is also known as the List Price.

Discount

A discount is a reduction given on the Marked Price (MP) of an article. It is always calculated on the Marked Price. The selling price is obtained after subtracting the discount from the marked price.
Discount = Marked Price (MP) – Selling Price (SP)

Successive Discounts

Sometimes, a seller offers more than one discount on an item. For instance, a discount of 20% followed by another discount of 10%. These are called successive discounts. It's crucial to remember that these are not simply added together (20% + 10% ≠ 30%). The second discount is applied to the price that results after the first discount has been applied.

Key Formulas for Profit and Loss

Formulas are the tools that help you solve problems quickly and accurately. Here is a list of all the essential formulas you must memorize.

• Profit % = (Profit / Cost Price) × 100
• Loss % = (Loss / Cost Price) × 100
• To find SP when CP and Profit % are given:
  SP = CP × [(100 + Profit %) / 100]
• To find SP when CP and Loss % are given:
  SP = CP × [(100 – Loss %) / 100]
• To find CP when SP and Profit % are given:
  CP = SP × [100 / (100 + Profit %)]
• To find CP when SP and Loss % are given:
  CP = SP × [100 / (100 – Loss %)]
• Discount % = (Discount / Marked Price) × 100
• To find SP when MP and Discount % are given:
  SP = MP × [(100 – Discount %) / 100]
• Formula for two Successive Discounts (d1% and d2%):
  Single Equivalent Discount = (d1 + d2 - (d1 × d2) / 100) %

Important Tricks and Shortcuts for SSC Exams

In a time-bound exam like SSC CGL, speed is everything. These shortcuts will help you save precious seconds.

1. Using Fractional Values of Percentages

Memorizing the fractional equivalents of common percentages can drastically speed up your calculations. For example:

• 20% = 1/5. A profit of 20% means if CP is 5 units, Profit is 1 unit, so SP is 6 units.
• 12.5% = 1/8. A loss of 12.5% means if CP is 8 units, Loss is 1 unit, so SP is 7 units.

Example: A man buys an article for ₹450 and sells it at a profit of 16.66%. Find the SP.
Solution: 16.66% = 1/6. This means if CP = 6 units, Profit = 1 unit. So, SP = 7 units.
Here, 6 units = ₹450 => 1 unit = ₹75.
Therefore, SP = 7 units = 7 × 75 = ₹525.

2. When Two Articles are Sold at the Same SP

If two articles are sold at the same Selling Price, one at a profit of x% and the other at a loss of x%, there is always an overall loss.
Overall Loss % = (x * x) / 100 = (x/10)² %

Example: A shopkeeper sells two watches for ₹990 each. On one, he gains 10% and on the other, he loses 10%. Find his overall gain or loss percent.
Solution: Here, x = 10. Using the formula, Overall Loss % = (10)² / 100 = 100 / 100 = 1% Loss.

3. The Dishonest Dealer Concept

A common question type involves a dishonest dealer who uses false weights to cheat customers. The formula to calculate their actual profit is:
Profit % = [(True Value - False Value) / False Value] × 100

Example: A dishonest shopkeeper professes to sell his goods at cost price but uses a weight of 800 gm instead of 1 kg. Find his profit percent.
Solution: Here, True Value = 1000 gm, False Value = 800 gm.
Profit % = [(1000 - 800) / 800] × 100 = (200 / 800) × 100 = (1/4) × 100 = 25%.

Solved Examples (Step-by-Step)

Let's apply these concepts and formulas to some typical SSC exam questions.

Example 1: Basic Profit Calculation

Question: Alfred buys an old scooter for ₹4700 and spends ₹800 on its repairs. If he sells the scooter for ₹5800, what is his gain percent?

Solution:
Step 1: Calculate the total Cost Price (CP).
CP = Purchase Price + Repair Cost = ₹4700 + ₹800 = ₹5500.
Step 2: Calculate the Profit.
Selling Price (SP) = ₹5800.
Profit = SP - CP = ₹5800 - ₹5500 = ₹300.
Step 3: Calculate the Profit Percentage.
Profit % = (Profit / CP) × 100
Profit % = (300 / 5500) × 100 = 300 / 55 = 60 / 11 = 5.45% (approx).
Answer: The gain percent is 5.45%.

Example 2: Finding Cost Price

Question: By selling an article for ₹720, a man loses 10%. At what price should he sell it to gain 5%?

Solution:
Step 1: Find the Cost Price (CP) using the initial SP and Loss %.
SP = ₹720, Loss % = 10%.
CP = SP × [100 / (100 – Loss %)]
CP = 720 × [100 / (100 – 10)] = 720 × (100 / 90) = 8 × 100 = ₹800.
Step 2: Calculate the new SP for the desired Profit %.
Desired Profit % = 5%.
New SP = CP × [(100 + Profit %) / 100]
New SP = 800 × [(100 + 5) / 100] = 800 × (105 / 100) = 8 × 105 = ₹840.
Answer: He should sell the article for ₹840 to gain 5%.

Example 3: Marked Price and Discount

Question: A trader marks his goods 40% above the cost price and allows a discount of 25%. What is his gain percent?

Solution:
Step 1: Assume a Cost Price (CP).
Let the CP be ₹100.
Step 2: Calculate the Marked Price (MP).
MP is 40% above CP.
MP = 100 + (40% of 100) = 100 + 40 = ₹140.
Step 3: Calculate the Selling Price (SP) after the discount.
Discount = 25% on MP.
Discount Amount = 25% of 140 = (25/100) × 140 = (1/4) × 140 = ₹35.
SP = MP - Discount = 140 - 35 = ₹105.
Step 4: Calculate the Gain Percent.
CP = ₹100, SP = ₹105.
Profit = SP - CP = 105 - 100 = ₹5.
Gain % = (Profit / CP) × 100 = (5 / 100) × 100 = 5%.
Answer: His gain percent is 5%.

Example 4: Successive Discounts

Question: Find the single discount equivalent to two successive discounts of 20% and 10%.

Solution:
Using the formula for successive discounts: d1 = 20%, d2 = 10%.
Single Equivalent Discount = (d1 + d2 - (d1 × d2) / 100) %
= (20 + 10 - (20 × 10) / 100) %
= (30 - 200 / 100) %
= (30 - 2) % = 28%.
Answer: The single equivalent discount is 28%.

Practice Questions for SSC CGL & CHSL

Now it's your turn! Solve these questions to test your understanding. The solutions are provided below.

1. A man buys a cycle for ₹1400 and sells it at a loss of 15%. What is the selling price of the cycle?
2. On selling 17 balls at ₹720, there is a loss equal to the cost price of 5 balls. What is the cost price of a ball?
3. A shopkeeper cheats to the extent of 10% while buying as well as selling, by using false weights. What is his total gain percent?
4. The marked price of a watch was ₹720. A man bought the same for ₹550.80 after getting two successive discounts, the first being 10%. What was the second discount rate?
5. If the cost price of 12 pens is equal to the selling price of 8 pens, what is the gain percent?
6. A vendor bought bananas at 6 for ₹10 and sold them at 4 for ₹6. Find his gain or loss percent.
7. A fruit seller sells mangoes at the cost price but still gains 25% by mixing something. What is the percentage of mixing?
8. An article is sold at a certain price. By selling it at 2/3 of that price, one loses 10%. Find the gain percent at the original price.
9. A person sold a horse at a gain of 15%. Had he bought it for 25% less and sold it for ₹600 less, he would have made a profit of 32%. What was the cost price of the horse?
10. A shopkeeper allows a 10% discount on his goods and still earns a profit of 20%. If the marked price is ₹800, what is the cost price?

Solutions to Practice Questions

Conclusion and Preparation Tips

Profit and Loss is a scoring and conceptually straightforward topic. The key to mastering it lies in understanding the core concepts and practicing a wide variety of questions. Start with the basics, memorize the formulas, and then move on to applying shortcuts. Regularly solve previous year question papers from SSC CGL and CHSL to get a feel for the types of questions asked. Remember, consistency is more important than intensity. Dedicate a specific amount of time each day to practice quantitative aptitude, and you will surely see a remarkable improvement. Good luck with your preparation!