Basic Word Problems
Word problems are real-life situations written in words that require mathematical reasoning to solve. They test not just calculation skills, but also understanding, interpretation, and logical thinking.
This lesson will teach you how to read word problems correctly, identify useful information, convert words into equations, and solve them step by step without confusion.
Why Word Problems Are Important
Word problems connect mathematics to the real world. They show how math is actually used in daily life, business, exams, and decision-making.
Almost every competitive exam includes word problems because they test true understanding.
Common Fear About Word Problems
Many students fear word problems because they look long and confusing at first glance.
In reality, word problems become easy once you learn how to break them into steps.
The Golden Rule of Word Problems
Never start calculating immediately. Always understand the situation first.
Math comes after understanding, not before.
Step-by-Step Method to Solve Any Word Problem
Every word problem — simple or complex — can be solved using the same logical steps.
- Read the problem carefully (at least twice)
- Identify what is given
- Identify what is asked
- Choose the correct operation
- Solve step by step
- Check if the answer makes sense
Understanding Keywords in Word Problems
Certain words indicate which mathematical operation to use. Recognizing them saves time in exams.
| Keyword | Operation |
| Total, sum, altogether | Addition |
| Difference, left, remaining | Subtraction |
| Each, times, product | Multiplication |
| Per, shared, equally | Division |
Addition Word Problems
Addition problems involve combining quantities. They usually include words like total, together, or sum.
Example: Ravi has 15 apples and buys 8 more. How many apples does he have now?
15 + 8 = 23 apples
Subtraction Word Problems
Subtraction problems involve removing or comparing quantities. Look for words like left, remaining, or difference.
Example: A shop had 50 pens. It sold 18 pens. How many pens are left?
50 − 18 = 32 pens
Multiplication Word Problems
Multiplication problems involve repeated groups or equal quantities. They often include words like each or times.
Example: There are 6 boxes, each with 9 chocolates. How many chocolates are there?
6 × 9 = 54 chocolates
Division Word Problems
Division problems involve sharing or grouping equally. Look for words like per, equally, or divided.
Example: 24 candies are shared equally among 6 children. How many does each get?
24 ÷ 6 = 4 candies
Word Problems with Multiple Steps
Some problems require more than one operation. These must be solved in the correct order.
Example: A man buys 3 notebooks at ₹20 each and pays ₹100. How much change does he get?
Cost = 3 × 20 = 60 Change = 100 − 60 = ₹40
Using Variables in Word Problems
When a value is unknown, we represent it using a variable like x or y.
This helps convert the word problem into an equation.
Example: A number increased by 5 gives 20 → x + 5 = 20
Word Problems in Daily Life
We solve word problems daily without realizing it.
- Shopping bills
- Travel planning
- Salary and expenses
- Cooking quantities
Math becomes meaningful through word problems.
Word Problems in Competitive Exams
Competitive exams often test:
- Speed + accuracy
- Correct operation selection
- Multi-step reasoning
Understanding the language is more important than fast calculation.
Common Mistakes to Avoid
Most mistakes happen due to rushing or misunderstanding.
- Using the wrong operation
- Ignoring units
- Not reading the full question
Slow reading saves time later.
Practice Questions
Q1. A book costs ₹45. How much will 7 books cost?
Q2. There are 120 students in a school. If 35 are absent, how many are present?
Q3. 48 chocolates are packed equally into 8 boxes. How many chocolates per box?
Quick Quiz
Q1. Which operation is used when quantities are shared equally?
Q2. What should you do first in a word problem?
Quick Recap
- Word problems connect math to real life
- Understanding comes before calculation
- Keywords help choose operations
- Step-by-step thinking avoids mistakes
- Practice improves confidence