Percentage Word Problems (Grade 5)
Percentage word problems apply your knowledge of percentages to real-life situations. These problems involve discounts, marks, attendance, savings, and more.
In Class 5, you will solve problems that require you to find the percentage of a number, calculate what percentage one number is of another, or find the original number when a percentage is given.
The key is reading the problem carefully, identifying what is given and what is asked, and choosing the right formula.
What is Percentage Word Problems - Class 5 Maths (Percentage)?
A percentage word problem is a real-life scenario described in words where you need to use percentage calculations to find the answer.
Three types of percentage problems:
- Type A: Find the percentage of a number. (What is 20% of 500?)
- Type B: Find what percentage one number is of another. (30 is what % of 150?)
- Type C: Find the whole when a percentage and part are given. (15% of what number is 45?)
Percentage Word Problems (Grade 5) Formula
Type A: Part = (Percentage / 100) × Whole
Type B: Percentage = (Part / Whole) × 100
Type C: Whole = Part × (100 / Percentage)
Discount problems:
- Discount amount = (Discount %) × (Marked Price) / 100
- Sale Price = Marked Price − Discount Amount
Profit and Loss (basic):
- Profit % = (Profit / Cost Price) × 100
- Loss % = (Loss / Cost Price) × 100
Types and Properties
Type 1: Discount problems
A shop offers a percentage off the original price.
Type 2: Exam/marks problems
Finding marks scored or percentage scored.
Type 3: Attendance problems
Finding how many students were present or absent.
Type 4: Savings and spending problems
Calculating how much was saved or spent from a total.
Type 5: Comparison problems
Comparing percentages across different totals.
Type 6: Increase and decrease problems
Finding the new value after a percentage increase or decrease.
Solved Examples
Example 1: Discount Problem
Problem: A pair of shoes is marked at ₹1,200. The shop gives a 25% discount. What is the sale price?
Solution:
Step 1: Discount = 25% of ₹1,200
Step 2: Discount = (25/100) × 1,200 = ₹300
Step 3: Sale price = ₹1,200 − ₹300 = ₹900
Answer: The sale price is ₹900.
Example 2: Exam Marks — Finding Percentage
Problem: Aditi scored 72 out of 80 in her Maths exam. What is her percentage?
Solution:
Step 1: Percentage = (72/80) × 100
Step 2: 72/80 = 9/10
Step 3: 9/10 × 100 = 90%
Answer: Aditi scored 90%.
Example 3: Attendance Problem
Problem: A school has 600 students. On a rainy day, only 75% attended. How many students were absent?
Solution:
Step 1: Students present = 75% of 600 = (75/100) × 600 = 450
Step 2: Students absent = 600 − 450 = 150
Answer: 150 students were absent.
Example 4: Savings Problem
Problem: Rahul's father earns ₹40,000 per month. He saves 15% of his income. How much does he save?
Solution:
Step 1: Savings = 15% of ₹40,000
Step 2: (15/100) × 40,000 = ₹6,000
Answer: He saves ₹6,000 per month.
Example 5: Finding the Whole Number
Problem: 20% of a number is 60. What is the number?
Solution:
Step 1: Let the number be N.
Step 2: 20% of N = 60 → (20/100) × N = 60
Step 3: N = 60 × (100/20) = 60 × 5 = 300
Answer: The number is 300.
Example 6: Price Increase
Problem: The price of a cricket bat was ₹800. It increased by 10%. What is the new price?
Solution:
Step 1: Increase = 10% of ₹800 = (10/100) × 800 = ₹80
Step 2: New price = ₹800 + ₹80 = ₹880
Answer: The new price is ₹880.
Example 7: Comparison Problem
Problem: Kavi scored 45 out of 50 in Hindi and 36 out of 40 in English. In which subject did he score a higher percentage?
Solution:
Step 1: Hindi: (45/50) × 100 = 90%
Step 2: English: (36/40) × 100 = 90%
Step 3: Both are equal at 90%.
Answer: Kavi scored equal percentages (90%) in both subjects.
Example 8: Multi-step — Total Bill After Discount
Problem: Meera buys a dress for ₹2,500 and a bag for ₹1,500. The shop gives a 20% discount on the total. What does she pay?
Solution:
Step 1: Total = ₹2,500 + ₹1,500 = ₹4,000
Step 2: Discount = 20% of ₹4,000 = (20/100) × 4,000 = ₹800
Step 3: Amount paid = ₹4,000 − ₹800 = ₹3,200
Answer: Meera pays ₹3,200.
Example 9: Population Decrease
Problem: A village had 5,000 people. Due to migration, the population decreased by 8%. What is the new population?
Solution:
Step 1: Decrease = 8% of 5,000 = (8/100) × 5,000 = 400
Step 2: New population = 5,000 − 400 = 4,600
Answer: The new population is 4,600.
Example 10: Tiffin Box Problem
Problem: Neha's tiffin box has 20 pieces of food. She ate 60% of them. How many pieces are left?
Solution:
Step 1: Pieces eaten = 60% of 20 = (60/100) × 20 = 12
Step 2: Pieces left = 20 − 12 = 8
Answer: 8 pieces are left.
Real-World Applications
Real-life situations involving percentage word problems:
- Shopping: Calculating discounts and final prices during sales.
- Exams: Finding percentage scores and comparing performance.
- Banking: Calculating simple interest on savings.
- Health: Understanding nutrition labels (e.g., 5% daily value of iron).
- Sports: Win/loss percentages, completion rates.
- Budget: Allocating percentages of income to savings, food, rent.
Key Points to Remember
- Read the problem twice. Identify: what is given and what is asked.
- Type A (find the part): Part = (Percentage/100) × Whole.
- Type B (find the percentage): Percentage = (Part/Whole) × 100.
- Type C (find the whole): Whole = Part × (100/Percentage).
- For discount problems: Sale Price = Marked Price − Discount.
- For increase/decrease: New Value = Original ± (Percentage × Original / 100).
- Always write units (₹, marks, students, kg) in your answer.
- Check: Does the answer make sense? A discount should make the price lower, not higher.
Practice Problems
- A book costs ₹450. A shop gives a 10% discount. What is the sale price?
- Dev scored 54 out of 60 in Science. What is his percentage?
- In a school of 1,000 students, 88% passed the exam. How many students failed?
- Priya saved 25% of her ₹3,200 pocket money. How much did she save?
- 30% of a number is 90. What is the number?
- The price of mangoes increased from ₹200 to ₹250 per kg. What is the percentage increase?
- A cricket team played 20 matches and won 70% of them. How many matches did they lose?
- Ria's monthly expenses are: 40% on food, 25% on rent, 15% on transport. If she earns ₹30,000, how much is left after these expenses?
Frequently Asked Questions
Q1. What are the three types of percentage word problems?
Type A: Find the percentage of a number (e.g., what is 20% of 500?). Type B: Find what percentage one number is of another (e.g., 40 is what % of 200?). Type C: Find the whole when the percentage and part are given (e.g., 25% of what number is 50?).
Q2. How do you calculate a discount?
Discount amount = (Discount % / 100) × Marked Price. Then, Sale Price = Marked Price − Discount. For example, 15% off ₹600: Discount = 15/100 × 600 = ₹90. Sale price = ₹600 − ₹90 = ₹510.
Q3. How do you find the percentage increase?
Percentage increase = [(New Value − Original Value) / Original Value] × 100. For example, if price goes from ₹200 to ₹230, increase = (30/200) × 100 = 15%.
Q4. How do you find the original number when a percentage is given?
Use the formula: Whole = Part × (100/Percentage). For example, if 20% of a number is 60, the number = 60 × (100/20) = 300.
Q5. What is the difference between percentage increase and percentage decrease?
Percentage increase means the value goes up (add the increase). Percentage decrease means the value goes down (subtract the decrease). Both use the same formula but with addition or subtraction.
Q6. How do you compare scores with different totals using percentages?
Convert each score to a percentage, then compare. For example, 36/40 = 90% and 42/50 = 84%. So 36/40 is the higher score despite the lower raw number.
Q7. Can the answer to a percentage word problem be a decimal?
Yes. For example, 15% of 75 = 11.25. Decimal answers are common and correct in percentage calculations.
Q8. What mistakes should I avoid in percentage word problems?
Common mistakes: (1) Confusing the part and the whole. (2) Forgetting to subtract the discount from the original price. (3) Using the wrong formula type. (4) Not including units in the answer.
Q9. How do I check my answer in a percentage word problem?
Use the reverse calculation. If you found 25% of 400 = 100, verify by checking: is 100 out of 400 equal to 25%? (100/400) × 100 = 25%. Correct.
