As the name suggests, the unitary method is used to first find the value of a single unit and then calculate the value of multiple units by multiplying the value of the single unit.
Suppose you buy one apple for ₹10. How much will it cost to buy 5 apples? The unitary method helps in solving such questions easily.
The unitary method is based on the concepts of ratio and proportion and is widely used in solving questions related to cost, distance, speed, wages, production, and daily-life calculations. It is an important topic for competitive exams such as SSC, RRB, Banking and other competitive exams.
Question 1: Rohan went to a stationery shop to purchase notebooks. He bought 3 notebooks for ₹36. What is the price of one notebook?
Solution:
Given,
Cost of 3 notebooks = ₹36
Using the unitary method,
Cost of 1 notebook (Since we are finding the cost of 1 notebook and we’re given the cost of 3 notebooks. Therefore, to find the cost of 1 notebook we have to divide because cost of 1 notebook will be less than cost of 3 notebooks)
= ₹36 ÷ 3
= ₹12
Therefore,
The price of one notebook is ₹12.
Question 2: A delivery rider covers 180 km using 4 litres of petrol. How much distance will he cover using 2.5 litres of petrol, assuming the fuel consumption remains the same?
Solution:
Given,
Distance covered using 4 litres of petrol = 180 km
Using the unitary method,
Distance covered using 1 litre of petrol
(Since we are finding the distance covered using 1 litre of petrol and we are given the distance covered using 4 litres of petrol, we have to divide to find the distance covered by 1 litre of petrol.)
= 180 ÷ 4
= 45 km
Now,
Distance covered using 2.5 litres of petrol
(Since we are finding the distance covered using 2.5 litres of petrol and we know the distance covered using 1 litre of petrol, we have to multiply.)
= 45 × 2.5
= 112.5 km
Therefore,
The delivery rider will cover 112.5 km using 2.5 litres of petrol.
Question 3: A customer purchased 12 bathing soaps for ₹192. What would be the cost of 15 such soaps if the price per soap remains the same?
Solution:
Given,
Cost of 12 bathing soaps = ₹192
Using the unitary method,
Cost of 1 bathing soap
(Since we are finding the cost of 1 bathing soap and we are given the cost of 12 bathing soaps, we have to divide to find the cost of 1 bathing soap.)
= ₹192 ÷ 12
= ₹16
Now,
Cost of 15 bathing soaps
(Since we are finding the cost of 15 bathing soaps and we know the cost of 1 bathing soap, we have to multiply.)
= ₹16 × 15
= ₹240
Therefore,
The cost of 15 bathing soaps is ₹240.
Question 4:
A school van covers 120 km in 3 hours.
(a) How much time will it take to cover 40 km at the same speed?
(b) How much distance will it cover in 5 hours at the same speed?
Solution:
Given,
Distance covered = 120 km
Time taken = 3 hours
(a) Time required to cover 40 km
Time required to cover 1 km
(Since we are finding the time required to cover 1 km and we are given the time required to cover 120 km, we have to divide.)
= 3 ÷ 120
= 1/40 hour
Now,
Time required to cover 40 km
(Since we are finding the time required to cover 40 km and we know the time required to cover 1 km, we have to multiply.)
= (1/40) × 40
= 1 hour
Therefore,
The school van will take 1 hour to cover 40 km.
(b) Distance covered in 5 hours
Distance covered in 1 hour
= 120 ÷ 3
= 40 km
Distance covered in 5 hours
= 40 × 5
= 200 km
Therefore,
The school van will cover 200 km in 5 hours.
Question 5: During a T20 cricket tournament, Amish scored 42 runs in 6 overs while Anoop scored 63 runs in 7 overs. Who scored more runs per over?
Solution:
Given,
Amish scored 42 runs in 6 overs.
Anoop scored 63 runs in 7 overs.
To find who scored more runs per over, we first find the runs scored in 1 over by each player.
Runs scored by Amish in 1 over
= 42 ÷ 6
= 7 runs
Runs scored by Anoop in 1 over
= 63 ÷ 7
= 9 runs
Now compare the runs scored per over.
Amish = 7 runs per over
Anoop = 9 runs per over
Since
9 > 7
Therefore,
Anoop scored more runs per over than Amish.
Question 6: A city received 360 mm of rainfall in 5 days during the monsoon season. Assuming the rainfall continues at the same rate, how much rainfall (in cm) will the city receive in 10 days?
Solution:
Given,
Rainfall in 5 days = 360 mm
Rainfall in 1 day
= 360 ÷ 5
= 72 mm
Rainfall in 10 days
= 72 × 10
= 720 mm
Since 10 mm = 1 cm, (Important: The rainfall obtained is 720 mm, but the answer is required in cm. Therefore, convert 720 mm into 72 cm before writing the final answer.)
720 mm
= 720 ÷ 10
= 72 cm
Therefore,
The city will receive 72 cm of rainfall in 10 days.
Question 7:
The cost of 6 kg of rice is ₹240.
(a) What will be the cost of 9 kg of rice?
(b) How many kilograms of rice can be purchased for ₹400?
Solution:
Given,
Cost of 6 kg of rice = ₹240
(a) Cost of 9 kg of rice
Cost of 1 kg of rice
= ₹240 ÷ 6
= ₹40
Cost of 9 kg of rice
= ₹40 × 9
= ₹360
Therefore,
The cost of 9 kg of rice is ₹360.
(b) Quantity of rice that can be purchased for ₹400
Cost of 1 kg of rice
= ₹40
Quantity of rice that can be purchased for ₹400
= ₹400 ÷ ₹40
= 10 kg
Therefore,
10 kg of rice can be purchased for ₹400.
Exam Tip:
In questions like this, first find the cost of 1 kg. Once the cost of 1 kg is known, you can easily find either:
- the cost of any quantity by multiplying, or
- the quantity that can be purchased for a given amount by dividing.
This is one of the most common applications of the unitary method in SSC, RRB, Banking, NDA, and CDS examinations.
Question 8: Aman purchased 12 notebooks for ₹180, while Rohit purchased 8 notebooks for ₹104. Who got the notebooks at a cheaper price per notebook?
Solution:
Given,
Aman purchased 12 notebooks for ₹180.
Rohit purchased 8 notebooks for ₹104.
To find who got the notebooks at a cheaper price, we first find the cost of 1 notebook for each person.
Cost of 1 notebook purchased by Aman
= ₹180 ÷ 12
= ₹15
Cost of 1 notebook purchased by Rohit
= ₹104 ÷ 8
= ₹13
Now compare the cost per notebook.
Aman = ₹15 per notebook
Rohit = ₹13 per notebook
Since
₹13 < ₹15
Therefore,
Rohit got the notebooks at a cheaper price per notebook.
Question 9: During the winter season, the average temperature in a hill station decreased by 18°C over a period of 36 days. If the temperature continues to decrease at the same rate, by how many degrees will it decrease in the next 12 days?
Solution:
Given,
Decrease in temperature in 36 days = 18°C
Decrease in temperature in 1 day
= 18 ÷ 36
= 0.5°C
Decrease in temperature in 12 days
= 0.5 × 12
= 6°C
Therefore,
The temperature will decrease by 6°C in the next 12 days.
Question 10: An NCC cadet riding a scooter used 4 litres of petrol to travel 200 km during a training camp. How many litres of petrol are required to travel 1 km?
Solution:
Given,
Petrol used = 4 litres
Distance travelled = 200 km
To find the petrol required to travel 1 km, we first find the petrol consumed per kilometre.
Petrol required to travel 1 km
= 4 ÷ 200 litres
= 0.02 litres
Therefore,
0.02 litres of petrol are required to travel 1 km.
Question 11: An examination authority printed 18,000 admit cards in 6 hours. If the printing continues at the same rate, how many admit cards can be printed in 10 hours?
Solution:
Given,
Number of admit cards printed in 6 hours = 18,000
Number of admit cards printed in 1 hour
= 18,000 ÷ 6
= 3,000
Number of admit cards printed in 10 hours
= 3,000 × 10
= 30,000
Therefore,
30,000 admit cards can be printed in 10 hours.
Question 12: A data entry operator engaged for an examination project earns ₹1,600 for 10 days of work. How much will the operator earn for 18 days of work at the same rate?
Solution:
Given,
Earnings for 10 days = ₹1,600
Earnings for 1 day
= ₹1,600 ÷ 10
= ₹160
Earnings for 18 days
= ₹160 × 18
= ₹2,880
Therefore,
The data entry operator will earn ₹2,880 for 18 days of work.
FAQ:
1. What is the unitary method and why is it useful?
The unitary method is a technique used to find the value of one unit first and then use it to find the value of multiple units.
For example, if the cost of 5 notebooks is ₹50, we can first find the cost of 1 notebook and then calculate the cost of any number of notebooks.
2. If 1 litre of petrol costs ₹90, how much will 0.5 litre of petrol cost?
Cost of 1 litre of petrol = ₹90
Cost of 0.5 litre of petrol
= ₹90 × 0.5
= ₹45
Therefore, 0.5 litre of petrol will cost ₹45.
3. Does the above example use the unitary method?
Yes.
We already know the cost of 1 litre of petrol, which is a single unit. Therefore, we multiply it by the required quantity (0.5 litre) to find the cost.
Hence, the example uses the unitary method.
4. Are unitary method questions asked in SSC, RRB, and other competitive examinations?
Yes.
Questions based on the unitary method are frequently asked in SSC, RRB, Banking, NDA, CDS, Defence, CSAT, and school examinations.
The concept is also used in topics such as:
- Ratio and Proportion
- Direct Proportion
- Inverse Proportion
- Time and Work
- Pipes and Cisterns
- Partnership
- Speed, Time and Distance
Therefore, learning the unitary method is important for competitive exam preparation.
5. What is the first step in the unitary method?
The first step is always to find the value of one unit.
For example:
If 5 kg of rice costs ₹200,
then
1 kg of rice
= ₹200 ÷ 5
= ₹40
Therefore, the value of one unit is ₹40.
Conclusion:
The unitary method is one of the most important concepts in arithmetic and aptitude. It helps us solve problems involving cost, distance, speed, wages, production, rainfall, and many real-life situations.
Important Resources to Ratio and Proportion
- Ratio and Proportion
- Basic Ratio Questions & Answers
- Ratio Word Problems with Answers
- Ratio Formula with Examples and Explanations
- Proportion Questions and Answers with Solutions
- Direct Proportion Questions and Answers
- Inverse Proportion Questions & Answers with Solutions
- Ratio and Proportion Practice Questions with Answers
- Ratio and Proportion PYQs SSC, RRB, Banking & Defence Exams (Solved)