Profit and Loss Problem Tricks: A Complete 2025 Guide for Competitive Exams

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Introduction

Here I will explain a few tricks for profit and loss problems. I gained this knowledge after writing years of competitive exams. Here I will explain when to use tricks and when to use the main method because sometimes tricks will consume more time than the main method, so we use the main method here, and vice versa (same, the main method consumes more time than the tricks, so we use tricks here). So we need to learn both because learning the concept is the main thing. It makes you understand the question, like what they are asking, what data they have given, and what we need to find. So here I will explain both the main method and trick. First the main method, then last about tricks.

First Let’s Learn Basic Profit and Loss Equations

Profit = SP – CP. (Selling Price – Cost Price)

Loss = CP – SP. (Cost Price – Selling Price)

Profit % = (Profit/CP) × 100. (We always calculate profit on cost price unless they are asking in the question like “calculate profit % on selling price,” then we calculate on the selling price. Unless the examiner mentions this, we calculate profit % on cost price.)

Loss % = (Loss/CP) × 100. (Same for the loss % also)

SP = (1 + Profit%) × CP

CP = SP / (1 + Profit%)

Problem on Profit and Loss

Now, this question is made by me — not asked in any competitive exam — but chances are there that they might ask this type of problem from profit and loss because it’s a subpart in it. Now the question is:

1) A man sells three articles X, Y, and Z for Rs. 1386 each. He sells article X at 12.5% loss, article Y at 10% profit. If there is no profit nor loss in the whole transaction, find the cost of article Z.

Solution:

Step 1:

First, let’s understand the question: what they are asking, what data they have given, and what we need to find.

A man sells three articles X, Y, Z for Rs. 1386 means: each article is sold at 1386. That is, X article is sold at 1386, Y article is sold at 1386, and article Z is sold at 1386. So 1386 is the selling price.

Next, he sells article X at 12.5% loss and article Y at 10% profit, which means: Here, article X is sold at a loss of 12.5%. Therefore, X is sold at 87.5% of its actual price (100% – 12.5% = 87.5%).

Here, article Y is sold at a profit of 10%. Therefore, Y is sold at 110% of its actual price (100% + 10% = 110%).

Next, if there is no profit nor loss in the whole transaction means: in the end they got neither profit nor loss. The reason is because of article Z. So we need to find the cost price of article Z.

Now, summary of the whole problem:

A man sells three articles X, Y, and Z, each for ₹1386.

He sells article X at a 12.5% loss.

He sells article Y at a 10% profit.

There is no overall profit or loss in the total transaction.

Question: What is the cost price of article Z?

Step 2:

Understand the Given Data

We are told:

• Selling Price (SP) of X = ₹1386
• Loss on X = 12.5%
• Selling Price of Y = ₹1386
• Profit on Y = 10%
• Selling Price of Z = ₹1386
• Overall transaction = No profit, no loss

So, the total cost price = total selling price of all 3 items combined.

Step 3:

Use Formula to Find Cost Price (CP) of Each Article

For Article X:

That means:

Selling Price = (1 – 1/8) × Cost Price

Loss = 12.5% = 1/8 (we can write 12.5% as 1/8)

Therefore SP = (7/8) × CP
(As I explained before, we assume CP as 1 or 100%. So to get selling price we subtract if it’s a loss or add if it’s profit from the CP. Here it’s a loss, so we subtract 1/8, which is 12.5% loss. Therefore we get selling price = 7/8 of cost price). So this is X article’s selling price.

Now X article’s selling price is 1386. Sub this in the above equation:

1386 = (7/8) × CP. Solving this, we get the cost price of X article:

CP of article X is ₹1584

For Article Y:

For article Y, we got profit. Therefore:

Profit = 10% = 1/10 (we can write 10% as 1/10)

That means:

Selling Price = (1 + 1/10) × Cost Price

Therefore SP = (11/10) × CP
(As I explained before, we assume CP as 1 or 100%. So to get selling price we subtract if it’s a loss or add if it’s profit from the CP. Here it’s profit, so we add 1/10, which is 10% profit. Therefore, we get selling price = 11/10 of cost price). So this is Y article’s selling price.

Now Y article’s selling price is 1386. Sub this in the above equation:

1386 = (11/10) × CP. Solving this, we get the cost price of Y article:

CP of article Y is ₹1260

Step 4:

Total Cost Price and Selling Price

Now add CP of X and Y:
Total CP of X and Y = 1584 + 1260 = ₹2844

We know there’s no profit or loss, so:
Total CP of all 3 items = Total SP of all 3 items

Now, Total SP of all 3 items = ₹1386 × 3 = ₹4158 (because each article is sold at 1386)

Now, to get article Z’s cost price, we need to subtract the X + Y articles’ cost price from 3 (X, Y, Z) articles’ selling price. That is:

CP of Z = 4158 − 2844 = ₹1314

Final Answer:

The cost price of article Z is ₹1314.

Therefore, we need to do this much process to get the answer, but learning the main concept is very important.

Now Method 2: Trick 1 to Solve Problems on Profit and Loss

It’s a ratio method: here we use fractions and ratios to find the answer in a short period of time.

For X:

X → CP and SP → CP:SP → 8:7
(Because 12.5% loss = 1/8. That is, CP is 8 parts and we got 1 part loss. Therefore, SP = 8 – 1 = 7 parts)

For Y:

Y → CP and SP → CP:SP → 10:11
(Because 10% profit = 1/10. That is, CP is 10 parts and we got 1 part profit. Therefore, SP = 10 + 1 = 11 parts)

But here X’s SP and Y’s SP are not the same. In the question, they said it’s equal. So now we make selling prices of X and Y equal.
How do we do that? Answer: By multiplying X with 11 and Y with 7.

Therefore,

• X → 88 : 77
• Y → 70 : 77

Now both X and Y’s selling prices are equal. From the question, we know that X, Y, and Z articles’ selling prices are equal. So from the question, we conclude that Z’s selling price is 77 parts. Because X and Y’s SP = 77 parts.

Therefore:

• X → 88 : 77
• Y → 70 : 77
• Z → ? : 77

To find Z’s cost price, we need to calculate X and Y’s profit/loss. Because in the question they said there is no profit or loss at the end.

Now I’ll explain this if you don’t understand how:

We got loss from article X. That is:

• CP = 88 parts
• SP = 77 parts
• Loss = 88 – 77 = 11 parts

Now, profit from article Y:

• CP = 70 parts
• SP = 77 parts
• Profit = 77 – 70 = 7 parts

Now calculate the overall profit/loss on both X and Y:

-11 + 7 = -4 parts (we got 4 parts as loss)

As mentioned in the question, there’s no profit or loss overall. That means we must get 4 parts profit on Z to make it neutral.

So we subtract 4 parts from the selling price of article Z to get the cost price of Z article (because we need to get profit). If it were a loss, we would add it. But here we need profit.

Z’s selling price is 77 parts. Now subtract 4 parts:

77 – 4 = 73 parts
→ 73 parts is the cost price of Z.

Now profit/loss is zero:
-11 + 7 + 4 = 0

If 77 parts = ₹1386 (as per question),
→ 1 part = ₹18
→ 73 parts = ₹1314

Therefore, cost price of Z is ₹1314

If you understand the concept, you can easily solve it.

Now Method 3: Trick 2 to Solve Problems on Profit and Loss

Try to guess the answer using divisibility rules.

After finding 1 part = 18, you can find the answer without calculating Z’s CP. Because X and Y’s SP is 77 parts = 1386, from this we get 1 part = 18.

18’s divisibility rule: Number must satisfy rules of 2 and 9
(If you don’t know divisibility rules, learn it — or I’ll make an article on it.)

Now check which option satisfies both:

For 1314:

Divisibility by 2: Ends with an even number
Divisibility by 9: Digital sum = 1 + 3 + 1 + 4 = 9

1314 is divisible by both 2 and 9

Therefore, 1314 is the correct answer.

Conclusion

Profit and loss problems can be confusing at first, but with the right approach and tricks, you can solve them easily and quickly. In the question we solved, we carefully used the cost price and selling price relationship, applied percentage loss and gain formulas, and balanced the overall transaction using the “no profit no loss” condition. This traditional method is useful not just for exams but also in real-life buying and selling scenarios.

📝 Homework Practice Question:

A man sells three articles A, B, and C for Rs. 1680 each.

• He sells article A at 15% loss,
• Article B at 20% profit,
• and makes no overall profit or loss in the whole transaction.

Find the cost price of article C.

Try to solve it using the same method we used in this article!

FAQs – Profit and Loss Problem Tricks

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