Read and understand word problems carefully to identify what is given and what is asked
Choose the correct operation(s) — addition, subtraction, multiplication, division
Solve multi-step problems that combine two or more concepts
Apply concepts of fractions, decimals, percentage, profit-loss, time-speed-distance, average, measurement, and geometry to real-life situations
Use the RUCSAC strategy (Read, Understand, Choose, Solve, Answer, Check)
Write clear solutions with proper steps and units
Verify answers using estimation or inverse operations
Introduction — Why Word Problems?
In real life, nobody gives you a sum like "245 + 378". Instead, you face situations: "If a train ticket from Delhi to Jaipur costs ₹245 and the return ticket costs ₹378, how much do both tickets cost together?" Word problems are where maths meets real life. They teach you to think, reason, and apply what you've learned.
In Class 5, word problems become more challenging. They often need two or more steps and combine concepts from different chapters — fractions with money, percentage with profit-loss, time with speed, area with cost, and more. The key skill is breaking a big problem into smaller steps.
Image needed: A visual showing the journey from a word problem to solution: a paragraph of text → identifying key info → choosing operation → calculating → writing the answer. Use Indian school children thinking with thought bubbles. Style: Flat illustration, step-by-step visual, colourful Size: 750×350px
The RUCSAC Strategy for Solving Word Problems
Follow this 6-step method for every word problem:
Step
Letter
What to Do
Example
1
Read
Read the problem carefully, at least twice
Understand the story/situation
2
Understand
Identify what is given and what is asked
Given: cost, quantity. Find: total cost
3
Choose
Decide which operation(s) to use
Multiply, then add
4
Solve
Do the calculations step by step
Show all working
5
Answer
Write the answer as a complete sentence with units
"Total cost = ₹575"
6
Check
Verify — does the answer make sense? Use estimation
Is ₹575 reasonable?
Think About It: The hardest part isn't the calculation — it's understanding what the problem is asking. Read carefully! Look for keywords like "total" (add), "remaining" (subtract), "each" (divide or multiply), "how much more" (subtract), "altogether" (add).
Keywords That Help You Choose the Operation
Operation
Keywords to Look For
Addition (+)
total, altogether, sum, combined, in all, both, together, increased by
Subtraction (−)
remaining, left, difference, less than, more than, how much more, decreased by, gave away
Multiplication (×)
each, per, every, times, groups of, rows of, total (when rate × quantity)
Division (÷)
shared equally, divided among, per person, how many groups, split into
Category 1: Money and Shopping Problems
These problems involve buying, selling, calculating totals, giving change, and managing budgets.
Example 1: Meena bought 3 notebooks at ₹45 each and 5 pens at ₹12 each. She gave ₹200 to the shopkeeper. How much change did she get?
Solution:
Step 1: Cost of notebooks = 3 × ₹45 = ₹135
Step 2: Cost of pens = 5 × ₹12 = ₹60
Step 3: Total cost = ₹135 + ₹60 = ₹195
Step 4: Change = ₹200 − ₹195 = ₹5
Example 2: A shopkeeper in Jaipur buys 50 kg of rice at ₹48 per kg and sells it at ₹56 per kg. Find his total profit.
Solution:
Cost Price (total) = 50 × ₹48 = ₹2,400
Selling Price (total) = 50 × ₹56 = ₹2,800
Profit = SP − CP = ₹2,800 − ₹2,400 = ₹400
Example 3: Priya saved ₹1,250 per month for 8 months. She spent ₹4,500 on books and ₹2,800 on a school bag. How much money does she have left?
Solution:
Total savings = 8 × ₹1,250 = ₹10,000
Total spent = ₹4,500 + ₹2,800 = ₹7,300
Money left = ₹10,000 − ₹7,300 = ₹2,700
Category 2: Fractions and Decimals
Example 4: Ravi had ₹600. He spent 1/3 of it on food and 1/4 of it on a book. How much money is left?
Solution:
Spent on food = 1/3 × ₹600 = ₹200
Spent on book = 1/4 × ₹600 = ₹150
Total spent = ₹200 + ₹150 = ₹350
Money left = ₹600 − ₹350 = ₹250
Example 5: A rope is 12.5 m long. If 3.75 m is cut off, and the remaining rope is divided into 5 equal pieces, what is the length of each piece?
Solution:
Remaining rope = 12.5 − 3.75 = 8.75 m
Length of each piece = 8.75 ÷ 5 = 1.75 m
Example 6: A tank is 3/5 full. It contains 240 litres of water. What is the full capacity of the tank?
Solution:
3/5 of capacity = 240 litres
1/5 of capacity = 240 ÷ 3 = 80 litres
Full capacity (5/5) = 80 × 5 = 400 litres
Category 3: Percentage Problems
Example 7: In a school of 800 students, 45% are girls. How many boys are there?
Solution:
Percentage of boys = 100% − 45% = 55%
Number of boys = 55% of 800 = (55/100) × 800 = 440 boys
Example 8: Arjun scored 72 out of 80 in Maths and 45 out of 50 in Science. In which subject did he score a higher percentage?
Solution:
Maths percentage = (72/80) × 100 = 90%
Science percentage = (45/50) × 100 = 90%
Both are equal at 90%
Example 9: A shirt costs ₹800. The shop gives a 15% discount. What is the selling price?
Solution:
Discount = 15% of ₹800 = (15/100) × 800 = ₹120
Selling price = ₹800 − ₹120 = ₹680
Category 4: Time, Speed, and Distance
Example 10: A bus travels from Pune to Mumbai (150 km) in 3 hours. It then travels from Mumbai to Surat (280 km) in 4 hours. What is the average speed for the entire journey?
Solution:
Total distance = 150 + 280 = 430 km
Total time = 3 + 4 = 7 hours
Average speed = 430 ÷ 7 = 61.4 km/h (approx.)
Example 11: Sita leaves home at 8:45 AM and reaches school at 9:20 AM. If the school is 2.1 km from her home, what is her average walking speed?
Solution:
Time taken = 9:20 − 8:45 = 35 minutes = 35/60 hours = 7/12 hours
Speed = Distance ÷ Time = 2.1 ÷ (7/12) = 2.1 × 12/7 = 25.2/7 = 3.6 km/h
Image needed: A visual map showing a bus route from Pune to Mumbai to Surat with distances (150 km, 280 km) and time (3 hrs, 4 hrs) marked on the route. Indian city names with highway markers. Style: Simple route map with colourful markers, child-friendly Size: 650×300px
Category 5: Measurement and Geometry
Example 12: A rectangular garden is 25 m long and 18 m wide. A path 2 m wide runs around the garden. Find the area of the path.
Solution:
Outer length = 25 + 2 + 2 = 29 m
Outer width = 18 + 2 + 2 = 22 m
Outer area = 29 × 22 = 638 m²
Inner area (garden) = 25 × 18 = 450 m²
Area of path = 638 − 450 = 188 m²
Example 13: A square room has a perimeter of 48 m. If tiling costs ₹85 per m², find the total cost of tiling the floor.
Solution:
Side of square = 48 ÷ 4 = 12 m
Area = 12 × 12 = 144 m²
Total cost = 144 × ₹85 = ₹12,240
Example 14: Ravi has a rectangular field 120 m long and 80 m wide. He wants to fence it with barbed wire. If fencing costs ₹25 per metre, and he puts 3 rounds of wire, find the total cost.
Solution:
Perimeter = 2 × (120 + 80) = 2 × 200 = 400 m
Total wire needed = 3 × 400 = 1,200 m
Total cost = 1,200 × ₹25 = ₹30,000
Image needed: Diagram of a rectangular garden (25m × 18m) with a 2m path around it. Show inner rectangle (garden) in green and outer path in grey with measurements labelled clearly. Style: Clean geometric diagram with dimensions, coloured Size: 550×400px
Category 6: Average and Data Problems
Example 15: The average marks of 40 students is 72. Later, 5 more students join with an average of 80. Find the new average of all 45 students.
Solution:
Total marks of 40 students = 40 × 72 = 2,880
Total marks of 5 new students = 5 × 80 = 400
New total = 2,880 + 400 = 3,280
New average = 3,280 ÷ 45 = 72.9 (approx.)
Example 16: In a cricket match, Team India scored 280 runs. Rohit scored 1/4 of the total, Virat scored 30% of the total, and the remaining runs were scored by other players. How many runs did other players score?
Example 17: 12 workers can build a wall in 10 days. How many days will 15 workers take to build the same wall?
Solution:
This is inverse proportion (more workers = less days)
12 workers → 10 days
1 worker → 10 × 12 = 120 days
15 workers → 120 ÷ 15 = 8 days
Example 18: If 5 kg of mangoes cost ₹375, find the cost of 8 kg of mangoes.
Solution:
Cost of 5 kg = ₹375
Cost of 1 kg = ₹375 ÷ 5 = ₹75
Cost of 8 kg = ₹75 × 8 = ₹600
Key Words
Word/Phrase
Meaning / Operation
Altogether / In all / Total
Addition
Remaining / Left over / Balance
Subtraction
Each / Per / Every / Times
Multiplication
Shared equally / Distributed / Per person
Division
How much more / How much less
Subtraction (comparison)
Fraction of
Multiply by fraction
Percentage of
Multiply by percentage/100
Profit / Loss
SP − CP or CP − SP
Average
Sum ÷ Number
Speed
Distance ÷ Time
Tips for Solving Word Problems
Always read the problem at least twice before starting
Underline the important numbers and what is being asked
Draw a picture or diagram if it helps (especially for geometry problems)
Break multi-step problems into smaller, simpler steps
Always include units in your answer (₹, km, kg, m², etc.)
Check: Does your answer make sense? Is it too big or too small?
Use estimation to verify — round numbers and check roughly
Write "Given", "To Find", and "Solution" clearly for long problems
Look for hidden information (e.g., "a dozen" = 12, "a pair" = 2)
In multi-step problems, the answer of one step often becomes the input for the next step
Finished learning? Now test what you know!
🎯 Quick Quiz — Test Yourself!
Answer these questions right here. You get instant feedback — no paper needed!
Score: 0 / 8
1. The keyword "altogether" in a word problem usually means you should:
"Altogether/total/in all" usually signals addition.
2. "Shared equally among" usually means you should:
Sharing equally means division.
3. Ravi had ₹500 and spent ₹320. How much is left?
500 − 320 = ₹180.
4. A box has 12 pens. How many pens are in 8 boxes?
12 × 8 = 96 pens.
5. Sita buys 3 books at ₹50 each. What is the total cost? (₹, digits only)
3 × ₹50 = ₹150.
6. 100 sweets are shared equally among 4 children. How many does each get?
100 ÷ 4 = 25 sweets each.
7. A shop sold 200 kg of rice on Monday and 250 kg on Tuesday. How much in total? (kg, digits only)
200 + 250 = 450 kg.
8. A rectangular garden is 15 m long and 10 m wide. What is its perimeter? (m, digits only)
Perimeter = 2 × (15 + 10) = 2 × 25 = 50 m.
Practice Questions
A. Money and Shopping
1. Sita bought 4 kg of apples at ₹180 per kg and 3 kg of oranges at ₹90 per kg. She paid with a ₹1,000 note. How much change did she receive?
2. A shopkeeper bought 200 pencils at ₹5 each and sold them at ₹7 each. Find his total profit.
3. Arjun's father earns ₹45,000 per month. He spends ₹18,000 on rent, ₹12,000 on food, ₹5,000 on education, and saves the rest. How much does he save in a year?
4. A family spent ₹3,200 on groceries, ₹1,800 on vegetables, and ₹950 on milk in one week. What is their monthly expenditure on food (assuming 4 weeks per month)?
5. Meena bought a table for ₹2,500 and spent ₹300 on polishing it. She sold it for ₹3,200. Did she make a profit or loss? How much?
B. Fractions and Decimals
1. A farmer has 240 hectares of land. He grows wheat on 2/5 of it, rice on 1/3, and vegetables on the rest. How many hectares are used for vegetables?
2. Priya had ₹1,500. She spent 2/5 on a dress and 1/6 on lunch. How much money is left?
3. A water tank holds 500 litres when full. It is currently 3/4 full. If 75.5 litres are used, how much water remains?
4. Ravi walks 2.75 km to school and 2.75 km back. How many km does he walk in 5 school days?
5. A book has 360 pages. Sita read 2/3 of it in the first week and 1/4 of the remaining in the second week. How many pages are still left?
C. Percentage and Discount
1. Out of 600 students, 72% passed the exam. How many students failed?
2. A bicycle costs ₹4,500. During a Diwali sale, a 20% discount is offered. What is the sale price?
3. Arjun scored 85% in Maths (total marks: 80), 90% in Science (total: 50), and 75% in English (total: 100). Find his total marks obtained.
4. A shirt's marked price is ₹950. First a 10% discount is given, then another 5% on the reduced price. What is the final price?
5. In a village, the population increased from 5,000 to 5,600 in one year. What is the percentage increase?
D. Time, Speed, and Distance
1. A car travels at 60 km/h for 2 hours and then at 80 km/h for 3 hours. Find the total distance and average speed.
2. A train 200 m long crosses a bridge 300 m long in 25 seconds. Find the speed of the train in km/h.
3. Meena starts cycling at 7:30 AM at a speed of 12 km/h. If her school is 6 km away, at what time will she reach?
4. Two trains start from Delhi and Mumbai (1,400 km apart) at the same time towards each other. One travels at 60 km/h and the other at 80 km/h. After how many hours will they meet?
5. Ravi covers half the distance to his office at 40 km/h and the other half at 60 km/h. Find his average speed for the whole journey.
E. Measurement and Geometry
1. A rectangular playground is 75 m long and 50 m wide. Find its perimeter and the cost of fencing at ₹45 per metre.
2. A square tile has a side of 30 cm. How many tiles are needed to cover a floor 3 m long and 2.4 m wide?
3. A room is 6 m long, 4.5 m wide, and 3 m high. If painting costs ₹35 per m², find the cost of painting all 4 walls.
4. A circular garden has a diameter of 14 m. Find the cost of putting a fence around it at ₹55 per metre. (Use π = 22/7)
5. A rectangular tank is 2 m long, 1.5 m wide, and 1 m deep. How many litres of water can it hold? (1 m³ = 1,000 litres)
F. Average and Data
1. The average of 5 numbers is 28. Four of them are 22, 30, 25, and 35. Find the fifth number.
2. A cricketer scored 45, 72, 38, 91, and 54 in 5 innings. Find his average. How many runs must he score in the 6th innings to raise his average to 65?
3. The average weight of a class of 35 boys is 42 kg and of 15 girls is 38 kg. Find the average weight of the whole class.
4. The temperature at 6 AM was 18°C. It increased by 2°C every hour till noon, then decreased by 1.5°C every hour till 6 PM. Find the average temperature from 6 AM to 6 PM.
5. Priya's marks in 6 subjects are: 78, 85, 92, 69, 88, and 76. If she needs an average of 82 to get a scholarship, does she qualify?
G. Unitary Method and Proportion
1. If 8 metres of cloth costs ₹1,200, find the cost of 13 metres.
2. A car uses 5 litres of petrol to travel 60 km. How much petrol is needed to travel 210 km?
3. If 6 workers can paint a house in 12 days, how many days will 9 workers take?
4. A factory produces 1,500 toys in 6 days. How many toys will it produce in 15 days?
5. If 3/4 kg of sweets costs ₹270, what is the cost of 2 kg?
H. Multi-Step Challenge Problems
1. A train leaves Delhi at 9:15 AM and reaches Agra (200 km away) at 11:45 AM. It stops for 30 minutes, then continues to Jaipur (240 km further) arriving at 3:15 PM. Find the average speed for each leg and the overall journey.
2. In a school, there are 1,200 students. 3/5 are boys. 40% of the boys and 60% of the girls take the school bus. How many students take the bus in total?
3. A merchant buys 100 oranges at ₹8 each. 10 oranges are spoiled and thrown away. He sells the remaining at ₹12 each. Find his profit percentage.
4. Ravi's rectangular garden is 30 m × 20 m. He wants to build a 1.5 m wide path inside along the boundary. If the path is cemented at ₹120 per m², find the total cost.
5. A family of 4 (father, mother, son, daughter) has an average age of 30. The father is 42, the mother is 38. The son is 3 years older than the daughter. Find the ages of the son and daughter.
Activity: Create Your Own Word Problems
Instructions:
Look around your home or neighbourhood for real-life maths situations.
Write 5 word problems based on real things (shopping bills, distances, time taken, etc.).
Make sure each problem uses a different concept (fractions, percentage, time, measurement, average).
Solve each problem yourself and write the answer key.
Exchange problems with a classmate and solve each other's!
Challenge: Create a 3-step word problem that combines money, percentage, AND fractions!
Image needed: Illustration of Indian students working together, writing word problems on paper with thought bubbles showing real-life scenes (shop, clock, measuring tape, garden). Colourful and collaborative. Style: Flat cartoon illustration, diverse Indian children, colourful Size: 650×400px
Want to review the lesson again?
Mathematics
Word Problems — Multi-Concept
Class 5 | CBSE / NCERT / ICSE
Name: Class: Date:
Word problems are where maths meets real life. They combine concepts from different chapters and require you to think carefully about what is given and what is asked. Use the RUCSAC strategy: Read, Understand, Choose operation, Solve, Answer with units, Check.
RUCSAC Strategy
Step
Action
Tip
R — Read
Read the problem twice
Don't rush
U — Understand
What's given? What's asked?
Underline key info
C — Choose
Which operation(s)?
Use keywords
S — Solve
Show all working
Step by step
A — Answer
Write with units
Complete sentence
C — Check
Does it make sense?
Use estimation
Keywords Guide
Operation
Keywords
Add (+)
total, altogether, sum, combined, in all, together
Subtract (−)
remaining, left, difference, how much more, gave away
Multiply (×)
each, per, every, times, groups of, total (rate × qty)
Divide (÷)
shared equally, per person, how many groups, split
Worked Examples
Ex 1 (Money): Meena bought 3 notebooks at ₹45 each and 5 pens at ₹12 each. She paid ₹200. Change?
