Profit, Loss & Discount: 10 Solved Word Problems

Hey future math whizzes! Ever sat in an exam, staring at a word problem involving a shopkeeper, a discounted shirt, and a tricky profit percentage, thinking, "Arey, what even is this?" You're not alone, yaar. Commercial mathematics, covering Profit, Loss, and Discount, can sometimes feel like a maze.

But guess what? It's one of the most practical and scoring topics you'll encounter in Class 7 and 8, for both CBSE and ICSE boards. It's not just about marks; it's about understanding how the real world works, from your local kirana store to big online sales. Today, we're going to demystify it with 10 solved problems, step-by-step!

Suno, this isn't just textbook stuff. Profit, Loss, and Discount are everywhere! When you buy a new phone on a festive sale, or your parents calculate the budget for a new appliance, or even when a company decides pricing for their products, these concepts are at play.

Understanding commercial math helps you make smarter decisions as a consumer and gives you a sneak peek into how businesses operate. Who knows, maybe one day you'll be running a big company, and these basics will be your best friend! It's foundational for future studies in commerce and even data science, where '73% of data science job postings require proficiency in statistics and linear algebra', and guess what, percentages are a huge part of that foundation!

Before we dive into problems, let's quickly brush up on the key terms, accha?

* Cost Price (CP): The price at which an article is bought. Think of it as the original investment.
* Selling Price (SP): The price at which an article is sold. This is what the customer pays.
* Profit: When $SP > CP$. Profit $= SP - CP$.
* Loss: When $CP > SP$. Loss $= CP - SP$.
* Profit/Loss Percentage: Calculated on CP.

Alright, let's get to the main event! Here are 4 typical problems you'll find in your ICSE (Selina Concise, S.Chand) and CBSE (NCERT, RD Sharma, RS Aggarwal) textbooks, broken down step-by-step. Pay close attention to how each variable is identified and used. We'll cover basic profit/loss, discount, and even GST!

Problem 1: Simple Profit Percentage

A shopkeeper bought a bicycle for Rs. 1500 and sold it for Rs. 1800. Find the profit percentage.

Solution:

1. Identify Given Values:
Cost Price (CP) = Rs. 1500
Selling Price (SP) = Rs. 1800

2. Calculate Profit:
Since $SP > CP$, there is a profit.
Profit = $SP - CP$
Profit = $1800 - 1500 = \text{Rs. } 300$

3. Calculate Profit Percentage:

Answer: The profit percentage is $20\%$.

Problem 2: Discount on Marked Price

The marked price of a jacket is Rs. 2500. A customer gets a discount of $10\%$ on it. What is the selling price of the jacket?

Solution:

1. Identify Given Values:
Marked Price (MP) = Rs. 2500
Discount Percentage = $10\%$

2. Calculate Discount Amount:
Discount = $10\%$ of MP
Discount = $\frac{10}{100} \times 2500$
Discount = $10 \times 25 = \text{Rs. } 250$

3. Calculate Selling Price (SP):
Selling Price = Marked Price - Discount
SP = $2500 - 250$
SP = $\text{Rs. } 2250$

Answer: The selling price of the jacket is Rs. 2250.

Problem 3: Finding CP with Profit/Loss

By selling a watch for Rs. 960, a shopkeeper incurs a loss of $4\%$. What was the cost price of the watch?

Solution:

1. Identify Given Values:
Selling Price (SP) = Rs. 960
Loss Percentage = $4\%$

2. Understand Loss Percentage Formula:
If there's a $4\%$ loss, it means the SP is $(100 - 4)\% = 96\%$ of the CP.
So, $96\%$ of CP = SP

3. Formulate Equation and Solve for CP:
$0.96 \times CP = 960$
$CP = \frac{960}{0.96}$
$CP = \frac{96000}{96}$
$CP = \text{Rs. } 1000$

Answer: The cost price of the watch was Rs. 1000.

Problem 4: GST Application

Rahul bought a washing machine for Rs. 18000 including $12\%$ GST. Find the price of the washing machine before GST was added.

Solution:

1. Identify Given Values:
Price including GST = Rs. 18000
GST Rate = $12\%$

2. Understand Price with GST:
If the original price (before GST) is $P$, then $P + 12\%$ of $P$ = Price including GST.
So, $P(1 + 0.12) = 1.12P$ = Price including GST.

3. Formulate Equation and Solve for Original Price (P):
$1.12 \times P = 18000$
$P = \frac{18000}{1.12}$
$P = \frac{1800000}{112}$
$P = 16071.428... \approx \text{Rs. } 16071.43$

Answer: The price of the washing machine before GST was added was approximately Rs. 16071.43.

Let's quickly sum up what we've learned today:

* Profit, Loss, and Discount are fundamental commercial math concepts with real-world applications.
* Always identify CP, SP, MP, and the percentage (profit, loss, or discount) correctly before starting.
* Profit/Loss is always calculated on CP, while Discount is always calculated on MP.
* GST adds to the original price, so $Price_{withGST} = Price_{original} \times (1 + \frac{GST\%}{100})$.
* Consistent practice, understanding concepts, and clear step-by-step solutions are crucial for mastering this topic.
* Believe in your abilities and keep practicing!

Here are some common questions students ask about this topic: