Understand what the Unitary Method is and when to use it
Find the value of ONE unit (Step 1) from a given quantity
Find the value of MANY units (Step 2) using the value of one unit
Identify Direct Variation (more → more) and solve related problems
Understand Inverse Variation (more → less) with simple examples
Solve multi-step word problems on cost, distance, time, and work
Apply the unitary method to real-life situations using Indian context
Introduction — What is the Unitary Method?
Imagine you go to a fruit seller in the market with your mother. A board says: "5 kg of mangoes = ₹400". You want to buy 8 kg. How much will that cost? Or imagine your father says: "1 pen costs ₹15". How much will 12 pens cost?
These everyday questions can be solved using the Unitary Method — one of the most useful techniques in mathematics!
The word "unitary" comes from "unit" which means one. In this method, we always find the value of ONE unit first, and then use it to find the value of as many units as we need.
The Two Steps of the Unitary Method
The unitary method always works in two simple steps:
The Golden Rule
Step 1: Find the value of ONE unit (divide the given value by the given number of units).
Step 2: Find the value of the required number of units (multiply the value of one unit by the required number).
Image needed: A step-by-step visual showing the unitary method process. Left side: "Given: 5 items cost ₹100". Middle: "Step 1: 1 item costs ₹100 ÷ 5 = ₹20" with a division arrow. Right side: "Step 2: 8 items cost ₹20 × 8 = ₹160" with a multiplication arrow. Use colourful boxes and arrows. Style: Clean infographic with 3 steps flowing left to right, bright colours, child-friendly Size: 800×350px
Example 1: If 5 kg of rice costs ₹250, find the cost of 8 kg of rice.
Step 1: Find the cost of 1 kg of rice.
Cost of 5 kg = ₹250
Cost of 1 kg = ₹250 ÷ 5 = ₹50
Step 2: Find the cost of 8 kg of rice.
Cost of 8 kg = ₹50 × 8 = ₹400
Answer: 8 kg of rice costs ₹400.
Example 2: If 1 pen costs ₹15, what is the cost of 12 pens?
Here, we already know the cost of 1 unit! So we only need Step 2.
Cost of 12 pens = ₹15 × 12 = ₹180
Answer: 12 pens cost ₹180.
Example 3: If 12 notebooks cost ₹540, find the cost of 7 notebooks.
Think About It: Why do we always find the value of ONE first? Because once you know the cost of 1 item, you can find the cost of ANY number of items simply by multiplying! This makes the unitary method extremely powerful and flexible.
Direct Variation (More → More, Less → Less)
In many real-life situations, when one quantity increases, the other quantity also increases. And when one quantity decreases, the other also decreases. This is called Direct Variation (or Direct Proportion).
Direct Variation — Remember!
More items → More cost
More distance → More time (at same speed)
More people → More food needed
More cloth → More money
Less items → Less cost
Image needed: A visual showing direct variation concept. Left side: 3 mangoes with ₹60 label. Right side: 9 mangoes with ₹180 label. Arrows showing "More mangoes → More money". A balance scale showing both sides going up together. Style: Colourful cartoon illustration, child-friendly, clear arrows and labels Size: 700×400px
Example 4: If 6 bananas cost ₹30, find the cost of 15 bananas.
Think: More bananas → More cost (Direct Variation)
Example 5: A car travels 240 km in 4 hours. How far will it travel in 7 hours at the same speed?
Think: More hours → More distance (Direct Variation)
Step 1: Distance in 1 hour = 240 ÷ 4 = 60 km Step 2: Distance in 7 hours = 60 × 7 = 420 km
Answer: The car will travel 420 km in 7 hours.
Example 6: If 8 metres of cloth costs ₹1,200, how much will 5 metres cost?
Think: Less cloth → Less cost (Direct Variation)
Step 1: Cost of 1 metre = ₹1,200 ÷ 8 = ₹150 Step 2: Cost of 5 metres = ₹150 × 5 = ₹750
Answer: 5 metres of cloth costs ₹750.
Example 7: A machine produces 350 toys in 5 days. How many toys will it produce in 12 days?
Think: More days → More toys (Direct Variation)
Step 1: Toys produced in 1 day = 350 ÷ 5 = 70 toys Step 2: Toys produced in 12 days = 70 × 12 = 840 toys
Answer: The machine will produce 840 toys in 12 days.
Inverse Variation (More → Less, Less → More)
Sometimes, when one quantity increases, the other quantity decreases. And when one decreases, the other increases. This is called Inverse Variation (or Inverse Proportion).
Inverse Variation — Remember!
More workers → Less time to finish work
More speed → Less time to cover the same distance
More taps filling a tank → Less time to fill it
Fewer workers → More time needed
Image needed: A visual showing inverse variation — a see-saw/balance concept. Left side: 4 workers finishing a wall in 6 days. Right side: 8 workers finishing the same wall in 3 days. Arrows showing "More workers → Less days". Use see-saw imagery to show the opposite movement. Style: Colourful cartoon illustration, see-saw balance, child-friendly, labelled arrows Size: 700×400px
Example 8: If 4 workers can paint a house in 12 days, how many days will 6 workers take to paint the same house?
Think: More workers → Less days (Inverse Variation)
Step 1: Find total work = 4 workers × 12 days = 48 worker-days
(This means the total work is equal to 1 worker working for 48 days.)
Step 2: If 6 workers do the same work:
Days needed = 48 ÷ 6 = 8 days
Answer: 6 workers will take 8 days to paint the house.
Example 9: If 5 students can clean a classroom in 20 minutes, how long will 10 students take?
Think: More students → Less time (Inverse Variation)
Step 1: Total work = 5 × 20 = 100 student-minutes Step 2: Time for 10 students = 100 ÷ 10 = 10 minutes
Answer: 10 students will take 10 minutes to clean the classroom.
Example 10: A car travelling at 60 km/h takes 4 hours to reach a city. How long will it take at 80 km/h?
Think: More speed → Less time (Inverse Variation)
Step 1: Total distance = 60 × 4 = 240 km Step 2: Time at 80 km/h = 240 ÷ 80 = 3 hours
Answer: At 80 km/h, the car will take 3 hours.
How to Tell the Difference:
Ask yourself: "If one thing increases, does the other also increase or decrease?"
• If both increase together → Direct Variation (divide, then multiply)
• If one increases while the other decreases → Inverse Variation (find total work/distance, then divide)
Unitary Method with Cost and Quantity
The most common use of the unitary method is in shopping and buying! Let us solve several examples involving cost and quantity.
Example 11: At a sabzi mandi (vegetable market), 4 kg of potatoes cost ₹120. Find the cost of 9 kg of potatoes.
Step 1: Cost of 1 kg = ₹120 ÷ 4 = ₹30 Step 2: Cost of 9 kg = ₹30 × 9 = ₹270
Answer: 9 kg of potatoes cost ₹270.
Example 12: Meena bought 6 packets of chips for ₹150. How much will 10 packets cost?
Example 15: Akriti bought 7 metres of ribbon for ₹84. How much ribbon can she buy for ₹156?
Step 1: Cost of 1 metre = ₹84 ÷ 7 = ₹12 Step 2: Ribbon for ₹156 = 156 ÷ 12 = 13 metres
Answer: She can buy 13 metres of ribbon for ₹156.
Example 16: At a book fair, 5 story books cost ₹625. Ravi has ₹1,000. How many story books can he buy?
Step 1: Cost of 1 book = ₹625 ÷ 5 = ₹125 Step 2: Books for ₹1,000 = 1,000 ÷ 125 = 8 books
Answer: Ravi can buy 8 story books with ₹1,000.
Unitary Method with Distance and Time
The unitary method is very useful when dealing with speed, distance, and time problems. Remember: Speed = Distance ÷ Time.
Example 17: A Rajdhani Express train covers 480 km in 6 hours. How far will it travel in 10 hours at the same speed?
Step 1: Distance in 1 hour (speed) = 480 ÷ 6 = 80 km/h Step 2: Distance in 10 hours = 80 × 10 = 800 km
Answer: The train will travel 800 km in 10 hours.
Example 18: Sita walks 3 km in 45 minutes. How long will she take to walk 7 km at the same speed?
Step 1: Time for 1 km = 45 ÷ 3 = 15 minutes Step 2: Time for 7 km = 15 × 7 = 105 minutes = 1 hour 45 minutes
Answer: Sita will take 1 hour 45 minutes to walk 7 km.
Example 19: A bus travels 150 km using 10 litres of diesel. How much diesel will it need for a 375 km trip?
Step 1: Diesel for 1 km = 10 ÷ 150 = 1/15 litre Step 2: Diesel for 375 km = (1/15) × 375 = 375 ÷ 15 = 25 litres
Answer: The bus will need 25 litres of diesel for 375 km.
Example 20: Hridan cycles 12 km in 48 minutes. How far can he cycle in 1 hour (60 minutes)?
Step 1: Distance in 1 minute = 12 ÷ 48 = 0.25 km = 250 metres Step 2: Distance in 60 minutes = 0.25 × 60 = 15 km
Answer: Hridan can cycle 15 km in 1 hour.
Unitary Method with Work and Workers
When a group of people (or machines) work together, we can use the unitary method to find how long a task will take with a different number of workers. This uses inverse variation.
Example 21: 6 workers can build a wall in 10 days. How many days will 15 workers take to build the same wall?
Think: More workers → Less days (Inverse Variation)
Step 1: Total work = 6 × 10 = 60 worker-days Step 2: Days for 15 workers = 60 ÷ 15 = 4 days
Answer: 15 workers will take 4 days to build the wall.
Example 22: 8 students can arrange a classroom in 30 minutes. How long will 12 students take?
Step 1: Total work = 8 × 30 = 240 student-minutes Step 2: Time for 12 students = 240 ÷ 12 = 20 minutes
Answer: 12 students will take 20 minutes.
Example 23: 3 taps can fill a tank in 8 hours. How long will 6 taps take to fill the same tank?
Step 1: Total work = 3 × 8 = 24 tap-hours Step 2: Time for 6 taps = 24 ÷ 6 = 4 hours
Answer: 6 taps will fill the tank in 4 hours.
Multi-Step Problems
Some problems require more than one application of the unitary method, or a combination of steps. Let us practice these harder problems.
Example 24: A school bought 8 boxes of chalk. Each box has 50 chalk sticks. If 400 chalk sticks cost ₹1,600, how much did the school spend on chalk?
First: Total chalk sticks = 8 × 50 = 400 sticks Given: 400 sticks cost ₹1,600. Answer: The school spent ₹1,600 on chalk.
Example 25: Bianca's family of 4 members uses 20 litres of milk in 5 days. How many litres of milk will a family of 6 members use in 8 days?
Step 1: Milk used by 4 members in 5 days = 20 litres
Milk used by 1 member in 5 days = 20 ÷ 4 = 5 litres
Milk used by 1 member in 1 day = 5 ÷ 5 = 1 litre
Step 2: Milk used by 6 members in 1 day = 1 × 6 = 6 litres
Milk used by 6 members in 8 days = 6 × 8 = 48 litres
Answer: A family of 6 will use 48 litres in 8 days.
Example 26: A farmer earns ₹4,500 in 9 days. He works 6 hours a day. How much does he earn per hour? How much will he earn in 15 days?
Part A — Per hour:
Earning in 9 days = ₹4,500
Earning in 1 day = ₹4,500 ÷ 9 = ₹500
Earning per hour = ₹500 ÷ 6 = ₹83.33 (approx.)
Part B — In 15 days:
Earning in 1 day = ₹500
Earning in 15 days = ₹500 × 15 = ₹7,500
Answer: He earns about ₹83.33 per hour and ₹7,500 in 15 days.
Example 27: A train covers 300 km in 5 hours. Another train covers the same 300 km in 4 hours. Which train is faster and by how much?
Train A: Speed = 300 ÷ 5 = 60 km/h Train B: Speed = 300 ÷ 4 = 75 km/h Difference: 75 − 60 = 15 km/h
Answer: Train B is faster by 15 km/h.
Word Problems — Indian Context
Let us solve real-life problems set in Indian situations — shopping at markets, travelling by trains, cooking for guests, and school activities.
Image needed: An Indian market scene (sabzi mandi) with price labels on fruits and vegetables. Labels show: "Onions ₹40/kg", "Tomatoes ₹60/kg", "Apples ₹180/kg", "Bananas ₹5 each". A child with a list and a thought bubble showing calculations. Style: Bright, colourful Indian market illustration, child-friendly, labelled price tags Size: 800×450px
Example 28: At Arjun's school canteen, 3 samosas cost ₹45. The teacher ordered samosas for 20 students (1 each). How much did she pay?
Example 29: A recipe for making 4 rotis uses 200 grams of atta (wheat flour). Priya's mother wants to make 14 rotis for dinner. How much atta does she need?
Example 30: The Shatabdi Express from Delhi to Chandigarh covers 250 km in 3 hours and 20 minutes. If a Vande Bharat train covers the same distance in 2 hours and 30 minutes, how far does the Vande Bharat travel in 1 hour?
For Vande Bharat:
Time = 2 hours 30 minutes = 2.5 hours
Speed = 250 ÷ 2.5 = 100 km/h
Answer: The Vande Bharat travels 100 km in 1 hour.
Example 31: During Diwali, Meena's family bought 12 diyas for ₹180. Her neighbour wants to buy 30 diyas from the same shop. How much will they cost?
A method where we first find the value of one unit, then use it to find the value of many units
Unit
One single item, one kilogram, one litre, one hour, etc.
Direct Variation
When one quantity increases, the other also increases (and vice versa)
Inverse Variation
When one quantity increases, the other decreases (and vice versa)
Rate
The cost or value per one unit (e.g., ₹15 per pen, 60 km per hour)
Proportion
Two quantities that change together in a fixed relationship
Worker-days
A way to measure total work (number of workers × number of days)
Speed
Distance covered per unit time (km/h, m/s)
Key Points to Remember
The Unitary Method has two steps: (1) Find value of ONE unit, (2) Find value of required units.
In Direct Variation: More → More. To find value of 1, divide. To find value of many, multiply.
In Inverse Variation: More → Less. Find total work first (multiply given values), then divide by the new quantity.
Always identify whether the problem is direct or inverse before solving.
The unitary method works with cost, distance, time, weight, workers, and any measurable quantity.
When finding "how many items can I buy," divide the total money by the cost of one item.
Check your answer: In direct variation, a bigger quantity should give a bigger value. In inverse variation, more workers should give less time.
Always write the units (₹, km, hours, litres, kg) with your answer.
Finished learning? Now test what you know!
🎯 Quick Quiz — Test Yourself!
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1. The unitary method first finds the value of:
Find the value of ONE first, then multiply for the amount you need.
2. If 5 pens cost ₹50, what does 1 pen cost?
₹50 ÷ 5 = ₹10 per pen.
3. More workers usually means the same job takes:
This is inverse variation — more workers, fewer days.
4. If 3 kg of rice cost ₹120, what do 6 kg cost?
1 kg = ₹40, so 6 kg = ₹240 (double of 3 kg).
5. If 4 notebooks cost ₹80, what do 10 notebooks cost? (₹, digits only)
1 notebook = 80 ÷ 4 = ₹20. 10 × ₹20 = ₹200.
6. A car travels 70 km on 1 litre. How far on 5 litres? (km, digits only)
70 km × 5 = 350 km.
7. If 1 worker would take 72 days to build a wall, how many workers are needed to finish it in 9 days?
1 worker → 72 days. To finish in 9 days you need 72 ÷ 9 = 8 workers.
8. If 8 metres of cloth cost ₹480, what is the cost of 1 metre? (₹, digits only)
₹480 ÷ 8 = ₹60 per metre.
Practice Questions
A. Find the cost:
1. If 4 kg of sugar costs ₹180, find the cost of 11 kg of sugar.
2. If 6 pencils cost ₹42, find the cost of 15 pencils.
3. If 9 litres of oil cost ₹1,350, find the cost of 4 litres.
4. If 5 metres of rope cost ₹75, find the cost of 22 metres.
5. If 3 dozen eggs cost ₹252, find the cost of 5 dozen eggs.
6. If 7 pens cost ₹189, find the cost of 20 pens.
B. Find the quantity:
1. If 5 kg of apples cost ₹600, how many kg can you buy for ₹1,080?
2. If 8 notebooks cost ₹360, how many can you buy for ₹630?
3. If 4 litres of paint cover 60 sq. metres, how many litres are needed for 105 sq. metres?
4. If ₹270 buys 6 metres of cloth, how many metres can ₹675 buy?
C. Direct Variation problems:
1. A car travels 180 km in 3 hours. How far will it travel in 7 hours?
2. A machine fills 120 bottles in 4 minutes. How many bottles will it fill in 15 minutes?
3. If 3 kg of wheat makes 9 rotis, how many rotis can be made from 8 kg of wheat?
4. A factory produces 560 biscuits in 7 hours. How many biscuits will it produce in 12 hours?
5. Ravi reads 45 pages in 3 days. How many pages will he read in 10 days?
D. Inverse Variation problems (simple):
1. If 4 workers can dig a trench in 18 days, how many days will 12 workers take?
2. If 6 pipes can fill a tank in 5 hours, how long will 10 pipes take?
3. A car travelling at 50 km/h takes 6 hours for a journey. How long will it take at 75 km/h?
E. Multi-step problems:
1. A family of 5 uses 10 kg of rice in 4 days. How much rice will a family of 3 use in 10 days?
2. A shop sells 4 pencil boxes at ₹120 each and 6 pens at ₹30 each. Find the total cost and the cost per item if all 10 items are counted together.
3. A train covers 200 km in 4 hours. After a 1-hour stop, it travels another 150 km in 3 hours. Find the average speed for the entire journey (including stop time).
4. Priya buys 3 kg of mangoes at ₹120/kg and 2 kg of grapes at ₹90/kg. How much does she spend in total? What is the average cost per kg of fruit?
F. Fill in the blanks:
1. If 7 items cost ₹350, then 1 item costs ₹.
2. If 1 kg of rice costs ₹55, then 9 kg costs ₹.
3. If 12 workers finish a job in 8 days, the total work is worker-days.
4. More items at the same rate means cost. (more / less)
5. More workers doing the same job means time. (more / less)
G. Choose the correct answer (MCQ):
1. If 5 books cost ₹200, the cost of 8 books is:
a) ₹280b) ₹320c) ₹300d) ₹360
2. If 3 workers finish a task in 12 days, then 6 workers will finish it in:
a) 24 daysb) 6 daysc) 4 daysd) 8 days
3. Which of the following is an example of inverse variation?
a) More pens → more costb) More speed → less timec) More cloth → more moneyd) More distance → more time
4. If 1 litre of milk costs ₹56, how much will 3.5 litres cost?
a) ₹168b) ₹196c) ₹182d) ₹210
H. Word Problems (Indian Context):
1. At a vegetable market in Delhi, 3 kg of onions cost ₹105. Anita needs 8 kg of onions for a family function. How much will she pay?
2. The Duronto Express covers 1,200 km from Mumbai to Delhi in 16 hours. What is its speed? How far will it travel in 10 hours?
3. For a school picnic, 5 buses can carry 250 students. How many buses are needed to carry 400 students?
4. Ravi's mother makes 6 glasses of mango lassi using 3 mangoes. If 15 guests are coming, how many mangoes does she need to make 15 glasses?
5. 9 labourers can harvest a field in 6 days. The farmer wants the harvesting done in 3 days because of expected rain. How many labourers does he need?
6. Dhruv's school ordered 45 cricket balls for ₹3,375. How much will 12 cricket balls cost for the inter-house tournament?
Activity — Market Day Calculator!
Imagine you are shopping at a market. Use the rate chart below to answer the questions:
Item
Rate
Rice
₹55 per kg
Dal (Toor)
₹140 per kg
Onions
₹35 per kg
Tomatoes
₹50 per kg
Milk
₹56 per litre
Bread
₹40 per packet
Eggs
₹7 per egg
Apples
₹180 per kg
Your Shopping List:
Item
Quantity Needed
Cost (Calculate!)
Rice
4 kg
Dal
2 kg
Onions
3 kg
Tomatoes
2 kg
Milk
3 litres
Bread
2 packets
Eggs
12 eggs
Apples
1.5 kg
Total Bill = ₹
Bonus: If you have ₹2,000, how much change will you get back? ₹
Want to review the lesson again?
Mathematics
Unitary Method (Advanced)
Class 5 | CBSE / NCERT / ICSE
Name: Class: Date:
Learning Objectives
Understand and apply the Unitary Method (find value of 1, then many)
Identify Direct Variation (more → more) and Inverse Variation (more → less)
Solve problems on cost, distance, time, and work
Apply unitary method to multi-step real-life word problems
What is the Unitary Method?
The Unitary Method is a technique where we first find the value of ONE unit, then use it to find the value of the required number of units. The word "unitary" comes from "unit" meaning one.
Example: If 5 kg of mangoes cost ₹400, what is the cost of 8 kg?
The Two Steps: Step 1: Find the value of ONE unit → Divide the given value by the given number of units. Step 2: Find the value of required units → Multiply the value of one unit by the required number.
[Image: Step-by-step unitary method process — Given → Step 1: Find value of 1 (divide) → Step 2: Find value of many (multiply)]
Worked Examples — Basic
Ex 1: 5 kg rice costs ₹250. Find cost of 8 kg.
Step 1: Cost of 1 kg = ₹250 ÷ 5 = ₹50
Step 2: Cost of 8 kg = ₹50 × 8 = ₹400
Ex 2: 12 notebooks cost ₹540. Find cost of 7 notebooks.
Step 1: Cost of 1 notebook = ₹540 ÷ 12 = ₹45
Step 2: Cost of 7 notebooks = ₹45 × 7 = ₹315
Ex 3: 6 bananas cost ₹30. Find cost of 15 bananas.
Step 1: Cost of 1 banana = ₹30 ÷ 6 = ₹5
Step 2: Cost of 15 bananas = ₹5 × 15 = ₹75
Direct Variation (More → More)
When one quantity increases, the other also increases. More items = more cost. More distance = more time. This is Direct Variation.
[Image: Direct variation visual — more mangoes on one side = more money on the other, with arrows showing both increasing together]
Ex 4: A car travels 240 km in 4 hours. Distance in 7 hours?
Step 1: Distance in 1 hour = 240 ÷ 4 = 60 km
Step 2: Distance in 7 hours = 60 × 7 = 420 km
Ex 5: 8 metres of cloth costs ₹1,200. Cost of 5 metres?
Step 1: Cost of 1 m = ₹1,200 ÷ 8 = ₹150
Step 2: Cost of 5 m = ₹150 × 5 = ₹750
Ex 6: A machine makes 350 toys in 5 days. Toys in 12 days?
Step 1: Toys in 1 day = 350 ÷ 5 = 70
Step 2: Toys in 12 days = 70 × 12 = 840 toys
Inverse Variation (More → Less)
When one quantity increases, the other decreases. More workers = less time. More speed = less time. This is Inverse Variation.
[Image: Inverse variation visual — see-saw showing more workers on one side means fewer days on the other side]
Method for Inverse Variation:
Step 1: Find TOTAL work = Given workers × Given days (or speed × time)
Step 2: Divide total work by new number of workers (or new speed)
Ex 7: 4 workers paint a house in 12 days. How many days for 6 workers?
Total work = 4 × 12 = 48 worker-days
Days for 6 workers = 48 ÷ 6 = 8 days
Ex 8: 5 students clean a room in 20 min. Time for 10 students?
Total work = 5 × 20 = 100 student-minutes
Time for 10 = 100 ÷ 10 = 10 minutes
Ex 9: A car at 60 km/h takes 4 hours. Time at 80 km/h?
Total distance = 60 × 4 = 240 km
Time at 80 km/h = 240 ÷ 80 = 3 hours
Unitary Method with Cost and Quantity
Ex 10: 4 kg potatoes = ₹120. Cost of 9 kg?
1 kg = ₹30 → 9 kg = ₹30 × 9 = ₹270
Ex 11: 8 litres milk = ₹360. Litres for ₹630?
1 litre = ₹45 → Litres for ₹630 = 630 ÷ 45 = 14 litres
Ex 12: 5 story books = ₹625. Books for ₹1,000?
1 book = ₹125 → Books = 1,000 ÷ 125 = 8 books
Distance, Time, and Work
Ex 13: Rajdhani covers 480 km in 6 hours. Distance in 10 hours?
Speed = 480 ÷ 6 = 80 km/h → In 10 hours = 80 × 10 = 800 km
Ex 14: Sita walks 3 km in 45 min. Time for 7 km?
1 km = 15 min → 7 km = 15 × 7 = 105 min = 1 hr 45 min
Ex 15: 6 workers build wall in 10 days. Days for 15 workers?
Total = 60 worker-days → 60 ÷ 15 = 4 days
Multi-Step Problems
Ex 16: Family of 4 uses 20 L milk in 5 days. Milk for 6 members in 8 days?
1 member, 1 day = 20 ÷ 4 ÷ 5 = 1 litre
6 members, 8 days = 1 × 6 × 8 = 48 litres
Ex 17: Farmer earns ₹4,500 in 9 days. Earning in 15 days?
1 day = ₹4,500 ÷ 9 = ₹500 → 15 days = ₹500 × 15 = ₹7,500
Word Problems — Indian Context
[Image: Indian market scene with price labels — onions ₹40/kg, tomatoes ₹60/kg, apples ₹180/kg, bananas ₹5 each]
Key Points to Remember:
• Unitary Method = Step 1: Find value of 1 (divide) → Step 2: Find value of many (multiply)
• Direct Variation: More → More. Divide then multiply.
• Inverse Variation: More → Less. Find total (multiply), then divide by new value.
• Always check: Does your answer make sense? More items should cost more (direct). More workers should take less time (inverse).
• Always write units with your answer (₹, km, hours, kg, litres).
• To find "how many can I buy": Divide total money by cost of 1 item.
Practice Questions
A. Find the cost:
1. If 4 kg sugar costs ₹180, find cost of 11 kg.
2. If 6 pencils cost ₹42, find cost of 15 pencils.
3. If 9 litres oil cost ₹1,350, find cost of 4 litres.
4. If 5 metres rope cost ₹75, find cost of 22 metres.
5. If 3 dozen eggs cost ₹252, find cost of 5 dozen.
6. If 7 pens cost ₹189, find cost of 20 pens.
B. Find the quantity:
1. 5 kg apples cost ₹600. How many kg for ₹1,080?
2. 8 notebooks cost ₹360. How many for ₹630?
3. 4 L paint covers 60 sq. m. Litres for 105 sq. m?
4. ₹270 buys 6 m cloth. Metres for ₹675?
C. Direct Variation problems:
1. Car travels 180 km in 3 hours. Distance in 7 hours?
2. Machine fills 120 bottles in 4 min. Bottles in 15 min?
3. 3 kg wheat makes 9 rotis. Rotis from 8 kg?
4. Factory: 560 biscuits in 7 hours. Biscuits in 12 hours?
5. Ravi reads 45 pages in 3 days. Pages in 10 days?
D. Inverse Variation problems:
1. 4 workers dig trench in 18 days. Days for 12 workers?
2. 6 pipes fill tank in 5 hours. Time for 10 pipes?
3. Car at 50 km/h takes 6 hours. Time at 75 km/h?
E. Multi-step problems:
1. Family of 5 uses 10 kg rice in 4 days. Rice for family of 3 in 10 days?
2. 4 pencil boxes at ₹120 each + 6 pens at ₹30 each. Total cost? Cost per item (all 10 items)?
3. Train: 200 km in 4 hrs, 1 hr stop, then 150 km in 3 hrs. Average speed for whole journey?
4. 3 kg mangoes at ₹120/kg + 2 kg grapes at ₹90/kg. Total? Average cost per kg?
F. Fill in the blanks:
1. If 7 items cost ₹350, then 1 item costs ₹.
2. If 1 kg rice costs ₹55, then 9 kg costs ₹.
3. If 12 workers finish a job in 8 days, total work = worker-days.
4. More items at same rate means cost. (more / less)
5. More workers doing same job means time. (more / less)
G. Choose the correct answer (MCQ):
1. If 5 books cost ₹200, cost of 8 books is:
a) ₹280b) ₹320c) ₹300d) ₹360
2. If 3 workers finish task in 12 days, 6 workers will finish in:
a) 24 daysb) 6 daysc) 4 daysd) 8 days
3. Which is inverse variation?
a) More pens → more costb) More speed → less timec) More cloth → more moneyd) More distance → more time
4. If 1 L milk costs ₹56, cost of 3.5 L is:
a) ₹168b) ₹196c) ₹182d) ₹210
H. Word Problems (Indian Context):
1. 3 kg onions cost ₹105. Cost of 8 kg for a family function?
2. Duronto covers 1,200 km in 16 hrs. Speed? Distance in 10 hrs?
3. 5 buses carry 250 students. Buses for 400 students?
4. 3 mangoes make 6 glasses lassi. Mangoes for 15 glasses?
5. 9 labourers harvest in 6 days. Labourers for 3 days?
6. 45 cricket balls = ₹3,375. Cost of 12 balls?
Activity — Market Day Calculator!
Use the rate chart to calculate your shopping bill:
Item
Rate
Qty Needed
Cost
Rice
₹55/kg
4 kg
Dal
₹140/kg
2 kg
Onions
₹35/kg
3 kg
Tomatoes
₹50/kg
2 kg
Milk
₹56/L
3 L
Bread
₹40/pkt
2 pkts
Eggs
₹7 each
12
Apples
₹180/kg
1.5 kg
Total = ₹Change from ₹2,000 = ₹
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