Unitary method questions with solutions are given here for students to practice and understand the concept of the unitary method. The unitary method is a basic concept to find the value of a single unit and then using that value to find the value of multiple units.
Learn more about Unitary Method.
Types of Unitary Method:
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Direct Variation |
The value of multiple units increases with an increase in the number of units. |
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Indirect/Inverse Variation |
The value of multiple units decreases with an increase in the number of units or vice-versa. |
Video Lesson on Unitary Method
Unitary Method Questions with Solutions
Following are some questions on unitary method of direct variation type.
Question 1: If the price of 5 kg potato is ₹ 150. Find the value of 24kg potato.
Solution:
Price of 5 kg potato = ₹ 150
Price of 1kg potato = ₹ 150/5 = ₹ 30
Price of 24 kg potato = 24 × 30 = ₹ 720
Question 2: A pack of 120 soaps is ₹ 540. Find the cost of 12 soaps.
Solution:
Cost of 120 soaps = ₹ 540
Cost of 1 soap = ₹ 540/120 = ₹ 4.5
Cost of 12 soaps = 4.5 × 12 = ₹ 54
Question 3: The length of the shadow of a 168 cm tall person at a particular time of day is 252 cm. What will be the length of the shadow of a 158 cm tall person at the same time of the day?
Solution:
Length of shadow for 168 cm = 252 cm
Length of the shadow for 1 cm = 252/168 = 1.5 cm
Length of the shadow for 158 cm = 1.5 × 158 = 237 cm.
Therefore, the length of the shadow for a 158 cm tall person is 237 cm.
Question 4: An iron rod of uniform thickness of length 5.6 m weighs 2.4 kg. How much will be the weight of 5 iron rods of the same thickness and length 8.4 m?
Solution:
Weight of 5.6 m rod = 2.4 kg
Weight of 1 m rod = 2.4 / 5.6 = 3/7 kg
Weight of 8.4 m rod = 3/7 × 8.4 = 3.6 kg
Weight of 5 such rods = 5 × 3.6 kg = 18 kg.
Question 5: The extension produced in an elastic wire on suspension of 94 kg weight is 2.24 m. What will be the extension produced in the wire of the same material when 72 kg weight is suspended?
Solution:
Extension produced on suspension of 94 kg weight = 0.47 m
Extension produced on suspension of 1 kg weight = 0.47/94 = 0.005 m
Extension produced on suspension of 72 kg weight = 0.005 × 72 = 0.36 m.
Also, Read:
Now, we shall solve some unitary method questions based on the inverse variation.
Question 6: 15 men can work together to finish a piece of work in 25 days. How many days will 20 men take to complete that same piece of work?
Solution:
Clearly, it is a case of inverse variation.
Number of days 15 men take to complete the work = 25 days
Number of days 1 man takes to complete the work = (25 × 15) = 375 days
Number of days 20 men take to complete the work = 375/20 = 18.75 ≈ 19 days
∴ 20 men will take approximately 19 days to complete the work.
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If M1 persons can finish a W1 units of work in D1 days working H1 hours a day and M2 persons can finish the W2 units of work in D2 days working H2 hours a day, then \(\begin{array}{l}\frac{M_{1}D_{1}H_{1}}{W_{1}}=\frac{M_{2}D_{2}H_{2}}{W_{2}}\end{array} \)
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Question 7: To complete a certain task 15 men take 10 days working 12 hours a day. How many hours a day should 10 men work to complete the same task in 20 days?
Solution:
Total work done by 15 men in 10 days working 12 hours a day = 15 × 10 × 12.
Let 10 men complete the task in 20 days working h hours a day.
Total work done by 10 men in 20 days working h hours a day = 10 × 20 × h
But, 15 × 10 × 12 = 10 × 20 × h
⇒ h = (15 × 10 × 12)/(10 × 20)
⇒ h = 9
∴ 10 men should work 9 hours a day to complete the task in 20 days.
Question 8: At a construction site, 4 men or 5 women can complete a task in 82 days. How many days will it take to complete the task by 5 men and 4 women?
Solution:
Let x be the work done by one man and y be the work done by one woman.
Then according to the question,
4x = 5y
⇒ x = 5y/4
Now, 5x + 4y = 5(5y/4) + 4y = 25y/4 + 4y
= 41y/4
If 5y can complete the task in 82 days
Then, 41y/4 can complete the task in 5y × 82 × 4/41y = 40 days.
∴ 5 men and 4 women can complete the task in 40 days.
Question 9: Two taps, A and B, can fill an empty tank in 30 hours and 15 hours, respectively. They both were turned on to fill the tank, but tap A was turned off after some time, and tap B took 12 hours to fill the tank. Find out after how much time tap A was turned off?
Solution:
Time taken by tap A to fill the tank = 30 hours
Portion of the tank filled by tap A in 1 h = 1/30
Time taken by tap B to fill the tank = 15 hours
Portion of the tank filled by tap B in 1 h = 1/15
Now, tap B ran for 12 hours, let tap A ran for x hours, then
x/30 + 12/15 = 1
⇒ x/30 + 24/30 = 1
⇒ x + 24 = 30
⇒ x = 30 – 24 = 6 hours.
∴ after 6 hours tap was turned off.
Question 10: A group of 120 men had provisions for 200 days. After 5 days, 30 men left. How long the provisions will last for the remaining men?
Solution:
According to the question,
The remaining provision is sufficient for 120 men up to 195 days.
Number of days provision for 1 man = 195 × 120 days
Number of days provision for (120 – 30) = 90 men = (195 × 120)/90 = 260 days
The provisions will last for 260 days.
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Practice Questions on Unitary Method
1. A herd of 45 cattle can graze a field in 13 days. How many of them can graze the same field in 9 days?
2. If 35 meters of cloth costs ₹ 1250. What will be the cost of 13 meters of the same cloth?
3. Travelling cost by bus for 125 km is ₹ 1050. How much will be the cost of travelling for 45 km?
4. A garrison had provision for 1500 men for 30 days. After some days, 300 more men joined the garrison. How many days the provisions will last?
5. Five men or ten women can complete a job in 20 days. In how many days can 3 men and 4 women can complete the same job?
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