Inverse Proportion Questions & Answers with Solutions
In the previous section, we covered different types of direct proportion questions and answers. In this section, we will practice important inverse proportion questions and answers.
Inverse proportion is an important concept in ratio and proportion. It helps us understand situations where one quantity increases while the other decreases.
For example, if more workers are assigned to a task, the time required to complete the work decreases.
The questions given below will help you understand the concept and learn how to apply it in different situations. Try solving each question on your own before checking the solution.
You can also visit our Ratio and Proportion, Ratio Formula with Examples and Explanations, Unitary Method Questions & Answers, and Direct Proportion Questions & Answers sections to strengthen your understanding of the topic.
Question 1: 20 workers take 4 days to complete laying a road. How many days will 10 workers take to complete laying the same length of road?
Solution:
Given,
Number of Workers (W₁)
= 20
Time Required (T₁)
= 4 days
Now,
Number of Workers (W₂)
= 10
Time Required (T₂)
= ?
Since fewer workers will take more time to complete the same road, the quantities are in inverse proportion.
In inverse proportion,
Workers ∝ 1/Days
Workers × Days = Constant
Or
W₁ × T₁ = W₂ × T₂
Therefore,
20 × 4 = 10 × x
80 = 10x
x = 80 ÷ 10
x = 8
Therefore,
10 workers will take 8 days to complete laying the same road.
Question 2: A railway training centre has enough drinking water for 30 trainees for 8 days. If 10 additional trainees join the programme, for how many days will the water last?
Solution:
Given,
Number of Trainees (T₁)
= 30
Number of Days (D₁)
= 8
Now,
Number of Trainees (T₂)
= 30 + 10
= 40
Number of Days (D₂)
= ?
Since more trainees will consume more water, the water will last for fewer days.
Therefore, the quantities are in inverse proportion.
In inverse proportion,
Trainees ∝ 1/Days
Therefore,
Trainees × Days = Constant
Or
T₁ × D₁ = T₂ × D₂
Substituting the values,
30 × 8 = 40 × x
240 = 40x
x = 240 ÷ 40
x = 6
Therefore,
The drinking water will last for 6 days.
Question 3: Four data entry operators can process a set of examination records in 6 days. If two more operators join the team and all operators work at the same efficiency, how many days will it take to complete the work?
Solution:
Given,
Number of Operators (O₁)
= 4
Number of Days (D₁)
= 6
Now,
Number of Operators (O₂)
= 4 + 2
= 6
Number of Days (D₂)
= ?
Since more operators can process the examination records faster, the work will be completed in fewer days.
Therefore, the quantities are in inverse proportion.
In inverse proportion,
Operators ∝ 1/Days
Therefore,
Operators × Days = Constant
Or
O₁ × D₁ = O₂ × D₂
Substituting the values,
4 × 6 = 6 × x
24 = 6x
x = 24 ÷ 6
x = 4
Therefore,
6 operators will complete the work in 4 days.
Question 4: An RRB candidate travels from Kanpur to Lucknow for an examination. At a speed of 60 km/h, the journey takes 2 hours. If the candidate travels at a speed of 80 km/h, how much time will the journey take?
Solution:
Given,
Speed (S₁)
= 60 km/h
Time (T₁)
= 2 hours
Now,
Speed (S₂)
= 80 km/h
Time (T₂)
= ?
Using the inverse proportion formula,
S₁ × T₁ = S₂ × T₂
Substituting the values,
60 × 2 = 80 × x
120 = 80x
x = 120 ÷ 80
x = 1.5
Therefore,
The candidate will take 1.5 hours (1 hour 30 minutes) to complete the journey.
SSC/RRB Shortcut:
60 × 2 = 120
120 ÷ 80 = 1.5 hours
Or
60×2= 80xX
X=1.5
Question 5: At an examination centre, 300 candidates are seated in 25 rows with 12 candidates in each row. If the seating arrangement is changed so that each row contains 20 candidates, how many rows will be required?
Solution:
Given,
Number of Candidates
= 300
Number of Rows (R₁)
= 25
Candidates per Row (C₁)
= 12
Now,
Candidates per Row (C₂)
= 20
Number of Rows (R₂)
= ?
Using the inverse proportion formula,
C₁ × R₁ = C₂ × R₂
Substituting the values,
12 × 25 = 20 × x
300 = 20x
x = 300 ÷ 20
x = 15
Therefore,
15 rows will be required.
Question 6: An SSC coaching institute conducts 8 classes per day, each lasting 45 minutes. If the institute decides to conduct 9 classes per day while keeping the total teaching time unchanged, what will be the duration of each class?
Solution:
Given,
Number of Classes (C₁)
= 8
Duration of Each Class (D₁)
= 45 minutes
Now,
Number of Classes (C₂)
= 9
Duration of Each Class (D₂)
= ?
Since the total teaching time remains unchanged, the number of classes and the duration of each class are in inverse proportion.
Using the inverse proportion formula,
C₁ × D₁ = C₂ × D₂
Substituting the values,
8 × 45 = 9 × x
360 = 9x
x = 360 ÷ 9
x = 40
Therefore,
The duration of each class will be 40 minutes.
Question 7: A small water pump can fill a storage tank at an RRB training centre in 3 hours, while a larger pump can fill the same tank in 2 hours. If both pumps are operated together, how long will it take to fill the tank?
Solution:
Given,
Time taken by the small pump
= 3 hours
Time taken by the large pump
= 2 hours
First, find the work done by each pump in 1 hour.
Work done by the small pump in 1 hour
= 1/3 of the tank
Work done by the large pump in 1 hour
= 1/2 of the tank
When both pumps operate together,
Work done in 1 hour
= 1/3 + 1/2
= (2 + 3)/6
= 5/6 of the tank
Therefore, time required to fill 1 tank
= 1 ÷ (5/6)
= 6/5 hours
= 1.2 hours
Converting 0.2 hour into minutes,
= 0.2 × 60
= 12 minutes
(Because 1 hour = 60 minutes)
Therefore,
1.2 hours
= 1 hour 12 minutes
Both pumps together will fill the tank in 1 hour 12 minutes.
Question 8: A railway canteen has enough food for 40 employees for 15 days. If 20 more employees join the project, for how many days will the food last?
Solution:
Given,
Number of Employees (E₁)
= 40
Number of Days (D₁)
= 15
Now,
Number of Employees (E₂)
= 40 + 20
= 60
Number of Days (D₂)
= ?
Using the inverse proportion formula,
E₁ × D₁ = E₂ × D₂
Substituting the values,
40 × 15 = 60 × x
600 = 60x
x = 600 ÷ 60
x = 10
Therefore,
The food will last for 10 days.
Question 9: An SSC coaching centre assigns a typing task to two operators. Ram can finish the task in 1 hour, while Shyam can finish the same task in 1.5 hours. If both work together, how much time will they take to complete the task?
Solution:
Given,
Time taken by Ram
= 1 hour
Time taken by Shyam
= 1.5 hours
First, find the work done by each operator in 1 hour.
Work done by Ram in 1 hour
= 1 task
Work done by Shyam in 1 hour
= 1 ÷ 1.5
= 2/3 task
When both work together,
Work done in 1 hour
= 1 + 2/3
= 5/3 tasks
Therefore, time required to complete 1 task
= 1 ÷ (5/3)
= 3/5 hour
= 0.6 hour
Converting 0.6 hour into minutes,
= 0.6 × 60
= 36 minutes
(Because 1 hour = 60 minutes)
Ram and Shyam together will complete the task in 36 minutes.
FAQ:
1. What is the inverse proportion?
When one quantity increases and the corresponding quantity decreases, or when one quantity decreases and the corresponding quantity increases, the quantities are said to be in inverse proportion.
For example if we increase the speed of our car to reach a destination we may reach there in less time. Or if we’re building a house and decrease the manpower, it will get completed in more days.
2. How do you identify an inverse proportion question?
If one quantity increases while the other decreases, then the quantities are in inverse proportion.
Some common examples are:
More Passengers → Water lasts fewer days
More Candidates per Row → Fewer Rows Required
Higher Speed → Less Travel Time
More Classes per Day → Shorter Class Duration
3. Are inverse proportion questions asked in various competitive exams like NDA, CDS, SSC, RRB etc?
Yes, inverse proportion questions are often asked in those competitive exams.
4. Are inverse proportion and direct proportion same?
No inverse proportion is just the opposite of direct proportion. In direct proportion:
More Students → More Study Notes
In inverse proportion:
Higher Speed → Less Travel Time
5. What is the formula for inverse proportion?
If two quantities X and Y are in inverse proportion, then:
X ∝ 1/Y
or
X₁Y₁ = X₂Y₂
Important Resources Related to Ratio and Proportion
- Ratio and Proportion
- Basic Ratio Questions & Answers
- Ratio Word Problems with Answers
- Ratio Formula with Examples and Explanations
- Direct Proportion Questions and Answers
- Unitary Method Questions and Answers with Solutions
- Proportion Questions and Answers with Solutions
- Ratio and Proportion Practice Questions with Answers
- Ratio and Proportion PYQs SSC, RRB, Banking & Defence Exams (Solved)
Conclusion:
Inverse proportion helps us solve problems where one quantity increases while the other decreases. It is commonly used in questions related to workers and time, speed and travel time, rows and seating arrangements, and resource allocation. By practicing these questions regularly, students can build a strong foundation in ratio and proportion.