Direct proportion is an important concept in ratio and proportion. In our previous section on unitary method questions and answers, we solved several questions to strengthen our understanding of ratio and proportion.
In this section, we will continue that learning by practicing important direct proportion questions and answers.
These questions are frequently asked in SSC, RRB, Banking, and other competitive examinations. Read each question carefully and try to solve it on your own before checking the solution.
Question 1: In two school libraries, the ratio of Mathematics books to Science books is 6 : 3 and 4 : 2 respectively. Are the book collections maintained in the same proportion?
Solution:
Given,
Ratio of Mathematics books to Science books in the first library
= 6 : 3
Ratio of Mathematics books to Science books in the second library
= 4 : 2
To determine whether the book collections are maintained in the same proportion, we compare the two ratios.
First Library Ratio
6 : 3
= 6/3
= 2/1
Second Library Ratio
4 : 2
= 4/2
= 2/1
So 6:3= 4:2
Since both ratios are equal, therefore, the proportion of Mathematics books to Science books is the same in both libraries.
For SSC/RRB shortcut:
6/3=2/1
4/2=2/1
So 6:3=4:2
Yes, the book collections are maintained in the same proportion.
Question 2: A map has a scale of 1 : 60,00,000. This means 1 cm on the map represents 60,00,000 cm on the ground. If the distance between two cities on the map is 5 cm, what is the actual distance between the cities in kilometres?
Solution:
Given,
Map Scale
= 1 : 60,00,000
This means,
1 cm on the map represents 60,00,000 cm on the ground.
Distance between the two cities on the map
= 5 cm
To find the actual distance, we use direct proportion.
If 1 cm on the map → 60,00,000 cm on the ground
Then 5 cm on the map → 60,00,000 × 5 cm
Actual distance = 3,00,00,000 cm
Therefore,
3,00,00,000 ÷ 100000 (because we know that 1 km = 100000 cm)
= 300 km
The actual distance between the two cities is 300 km.
Question 3: A coaching institute prepares an energy drink for students using 6 scoops of glucose powder, 3 scoops of electrolyte mix, and 9 scoops of protein supplement. Another batch needs to prepare the same drink but has only 2 scoops of glucose powder available. How many scoops of the other ingredients should be used to maintain the same mixture?
Solution:
Given,
Glucose Powder : Electrolyte Mix : Protein Supplement
= 6 : 3 : 9
Another batch has only 2 scoops of glucose powder available.
Since the second batch wants to prepare the same energy drink, the proportion of all ingredients must remain unchanged.
In the first mixture, 6 scoops of glucose powder are used.
In the second mixture, only 2 scoops of glucose powder are available.
Since the second batch wants to prepare the same energy drink, all ingredients must be reduced in the same ratio to maintain the same mixture.
However, we do not know the quantities of electrolyte mix and protein supplement in the second mixture. We only know that:
6 scoops of glucose powder in the first mixture and 2 scoops of glucose powder in the second mixture.
Therefore, we first compare the quantity of glucose powder in the two mixtures.
2/6 = 1/3
This means that the second mixture is one-third of the first mixture.
Since the mixture must remain the same, every ingredient must be multiplied by the same factor:
1/3
Therefore,
Electrolyte Mix
= 3 × 1/3
= 1 scoop
Protein Supplement
= 9 × 1/3
= 3 scoops
1 scoop of electrolyte mix and 3 scoops of protein supplement should be used.
SSC/RRB shortcut:
6 → 2
Scale Factor = 2/6 = 1/3
3 × 1/3 = 1
9 × 1/3 = 3
Question 4: An examination authority prints admit cards using three coloured inks in the ratio Red : Blue : White = 2 : 3 : 5. If 10 litres of white ink are used, how many litres of red ink and blue ink are required to maintain the same colour proportion?
Solution:
Given,
Red : Blue : White
= 2 : 3 : 5
White Ink = 10 litres
Since 5 parts correspond to 10 litres,
1 part = 10 ÷ 5
= 2 litres
Therefore,
Red Ink
= 2 × 2
= 4 litres
Blue Ink
= 3 × 2
= 6 litres
Red Ink = 4 litres
Blue Ink = 6 litres
Question 5: A construction company prepares concrete by mixing cement, sand, and gravel in the ratio 1 : 1.5 : 3. If 3 bags of cement are available, how many bags of sand and gravel are required to maintain the same mixture? Also, find the total number of bags in the mixture.
Solution:
Given,
Cement : Sand : Gravel
= 1 : 1.5 : 3
Available Cement
= 3 bags
Since the mixture must remain the same, all components must increase in the same proportion.
In the given ratio,
1 part of cement corresponds to 3 bags of cement
Therefore, the scale factor is:
3 ÷ 1 = 3
Now multiply each component by 3.
Sand
= 1.5 × 3
= 4.5 bags
Gravel
= 3 × 3
= 9 bags
Total bags in the mixture
= 3 + 4.5 + 9
= 16.5 bags
Sand Required = 4.5 bags
Gravel Required = 9 bags
Total Mixture = 16.5 bags
SSC/RRB Shortcut:
Scale Factor = 3 ÷ 1 = 3
Sand = 1.5 × 3 = 4.5 bags
Gravel = 3 × 3 = 9 bags
Total:
3 + 4.5 + 9 = 16.5 bags
Question 6: During an art competition, a special shade of purple is prepared by mixing red, blue, and white colours in the ratio 2 : 3 : 5. If a student needs 50 ml of this purple colour, how many ml of red, blue, and white colours should be mixed?
Solution:
Given,
Red : Blue : White
= 2 : 3 : 5
Total Purple Colour Required
= 50 ml
First, find the total number of parts.
2 + 3 + 5
= 10 parts
Since 10 parts correspond to 50 ml,
1 part = 50 ÷ 10
= 5 ml
Now find the quantity of each colour.
Red Colour
= 2 × 5
= 10 ml
Blue Colour
= 3 × 5
= 15 ml
White Colour
= 5 × 5
= 25 ml
Red Colour = 10 ml
Blue Colour = 15 ml
White Colour = 25 ml
Question 7: At an RRB coaching centre in Kanpur, a daily study session is divided among Mathematics, Reasoning, General Awareness, and Current Affairs in the ratio 3 : 4 : 3 : 5. If the total study session lasts 150 minutes, how much time is allocated to each subject?
Solution:
Given,
Ratio of time allocated to:
Mathematics : Reasoning : General Awareness : Current Affairs
= 3 : 4 : 3 : 5
Total Study Session
= 150 minutes
First, find the total number of parts.
3 + 4 + 3 + 5
= 15 parts
Since 15 parts correspond to 150 minutes,
1 part = 150 ÷ 15
= 10 minutes
Now find the time allocated to each subject.
Mathematics
= 3 × 10
= 30 minutes
Reasoning
= 4 × 10
= 40 minutes
General Awareness
= 3 × 10
= 30 minutes
Current Affairs
= 5 × 10
= 50 minutes
Mathematics = 30 minutes
Reasoning = 40 minutes
General Awareness = 30 minutes
Current Affairs = 50 minutes
Question 8: A railway recruitment library near Kanpur Central Railway Station has study materials in the ratio of RRB books : SSC books : Banking books = 3 : 2 : 1. If the library has 288 RRB books, how many SSC and Banking books does it have?
Solution:
Given,
RRB Books : SSC Books : Banking Books
= 3 : 2 : 1
Number of RRB Books
= 288
In the given ratio,
3 parts correspond to 288 RRB books
Therefore,
1 part = 288 ÷ 3
= 96 books
Now find the number of books in the other categories.
SSC Books
= 2 × 96
= 192 books
Banking Books
= 1 × 96
= 96 books
SSC Books = 192
Banking Books = 96
SSC/RRB Shortcut:
3 parts = 288
1 part = 288 ÷ 3
= 96
Therefore,
SSC Books = 2 × 96 = 192
Banking Books = 1 × 96 = 96
Question 9: At a ticket counter near Hisar Railway Station, the number of ₹10, ₹5, ₹2, and ₹1 coins in the cash box is in the ratio 4 : 3 : 2 : 1. If there are 100 coins in total, what is the total value of all the coins?
Solution:
Given,
Ratio of ₹10 coins : ₹5 coins : ₹2 coins : ₹1 coins
= 4 : 3 : 2 : 1
Total Number of Coins
= 100
First, find the total number of parts.
4 + 3 + 2 + 1
= 10 parts
Therefore,
1 part = 100 ÷ 10
= 10 coins
Now find the number of coins of each denomination.
₹10 Coins
= 4 × 10
= 40 coins
₹5 Coins
= 3 × 10
= 30 coins
₹2 Coins
= 2 × 10
= 20 coins
₹1 Coins
= 1 × 10
= 10 coins
Now calculate the value of each type of coin.
Value of ₹10 Coins
= 40 × 10
= ₹400
Value of ₹5 Coins
= 30 × 5
= ₹150
Value of ₹2 Coins
= 20 × 2
= ₹40
Value of ₹1 Coins
= 10 × 1
= ₹10
Total Value of Coins
= 400 + 150 + 40 + 10
= ₹600
Question 10: An SSC coaching institute prints 600 study notes for 30 students. How many study notes are required for 50 students if every student receives the same number of notes?
Solution:
Given,
Number of Students
= 30
Number of Study Notes
= 600
To find the number of study notes required for 50 students, we first find the number of study notes required for 1 student.
Study Notes for 1 Student
= 600 ÷ 30
= 20
Since every student receives the same number of notes,
Study Notes for 50 Students
= 20 × 50
= 1000
1,000 study notes are required for 50 students.
Question 11: At Lucknow Junction Railway Station, a drinking water kiosk serves 300 passengers using 600 litres of water per day. If the number of passengers increases to 450 and the average water consumption per passenger remains the same, how many litres of water will be required per day?
Solution:
Given,
Number of Passengers
= 300
Water Consumed
= 600 litres per day
To find the water required for 450 passengers, we first find the water consumed by 1 passenger.
Water Consumed by 1 Passenger
= 600 ÷ 300
= 2 litres
Since the average water consumption per passenger remains the same,
Water Required for 450 Passengers
= 2 × 450
= 900 litres
900 litres of water will be required per day.
FAQ
1. What is the direct proportion?
When one quantity increases or decreases, the other quantity also increases or decreases in the same ratio, then the quantities are said to be in direct proportion.
For example, if 10 notebooks cost ₹50, then 20 notebooks will cost ₹100.
2. How do you identify a direct proportion question?
If one quantity increases and the corresponding quantity also increases, or if one quantity decreases and the corresponding quantity also decreases, then it is a direct proportion question.
3. What is the formula of direct proportion?
If x is increasing or decreasing = Y increasing or decreasing. Or
If two quantities x and y are in direct proportion, then
x/y = constant
4. Are direct proportion questions asked in SSC and RRB exams?
Yes, direct proportion questions are asked in SSC and RRB examinations every year.
5. What is the difference between direct and inverse proportion?
In direct proportion, both quantities increase or decrease together. In inverse proportion, one quantity increases while the other decreases.
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
- Unitary Method Questions and Answers with Solutions
- Proportion Questions and Answers with Solutions
- Inverse Proportion Questions & Answers with Solutions
- Ratio and Proportion Practice Questions with Answers
- Ratio and Proportion PYQs SSC, RRB, Banking & Defence Exams (Solved)