We have already covered the basics of proportion in our Ratio and Proportion section. In this chapter, we will practice important proportion questions and answers to strengthen our understanding of the concept and learn how to apply it in different situations.
These questions are frequently asked in SSC, RRB, Banking, Defence, NDA, CDS, school examinations, and other competitive exams.
If you are new to this topic, we recommend first reading our Ratio and Proportion section. To understand the important formulas used in solving these questions, you can also check our Ratio Formula with Examples and Explanations page.
By solving the questions given below, you will develop a strong understanding of proportions, equivalent ratios, missing-term problems, and other common applications of proportion.
Once you complete this section, you will be able to solve a wide variety of proportion questions confidently and accurately.
Question 1:
A coaching institute reports that the ratio of selected to appeared candidates in Batch A is 35 : 49. In Batch B, the ratio is 50 : 70.
Are these ratios in proportion?
Answer
According to the definition of proportion,
Two ratios are said to be in proportion if they are equal.
Given,
35 : 49
and
50 : 70
Using the ratio formula,
35/49
= 5/7
and
50/70
= 5/7
Since
35/49 = 50/70
Therefore,
35 : 49 = 50 : 70
Hence, the given ratios are in proportion.
Question 2:
Are 24, 36, 40 and 60 in proportion?
Answer
According to the definition of proportion,
Four numbers a, b, c and d are said to be in proportion if
a : b = c : d
Given,
a = 24
b = 36
c = 40
d = 60
To check whether these numbers are in proportion, we verify whether
a : b = c : d
Substituting the values,
24 : 36 = 40 : 60
Using the ratio formula,
24/36
= 2/3
and
40/60
= 2/3
Since
24/36 = 40/60
Therefore,
24 : 36 = 40 : 60
Hence, 24, 36, 40 and 60 are in proportion.
Question 3: Do the ratios 24 cm : 4 m and 15 seconds : 5 minutes form a proportion?
Answer
We know from the definition of proportion that two ratios are said to be in proportion if they are equal.
Given,
24 cm : 4 m
and
15 seconds : 5 minutes
Before comparing the ratios, we must convert the quantities into the same units.
According to the Ratio Formula, a ratio compares two quantities of the same kind. Therefore, both quantities in a ratio must be expressed in the same unit.
First Ratio
4 m = 400 cm
Therefore,
24 cm : 400 cm
= 24/400
= 3/50
Second Ratio
5 minutes = 300 seconds
Therefore,
15 seconds : 300 seconds
= 15/300
= 1/20
Now compare the two ratios.
3/50 ≠ 1/20
Therefore,
24 cm : 4 m ≠ 15 seconds : 5 minutes
Hence, the given ratios do not form a proportion.
Answer: No, the given ratios do not form a proportion.
Question 4: The cost of 3 kg of oranges is ₹240 and the cost of 6 kg of oranges is ₹480. Are the quantities 3, 240, 6 and 480 in proportion?
Answer
Four numbers a, b, c and d are said to be in proportion if
a : b = c : d
Given,
a = 3
b = 240
c = 6
d = 480
To check whether these numbers are in proportion, we verify whether
a : b = c : d
Substituting the values,
3 : 240 = 6 : 480
Using the ratio formula,
3/240
= 1/80
and
6/480
= 1/80
Since
3/240 = 6/480
Therefore,
3 : 240 = 6 : 480
Hence, 3, 240, 6 and 480 are in proportion.
Question 5: An SSC aspirant solves 45 questions in 3 hours. At the same speed, can he solve 75 questions in 5 hours?
Answer
Given here,
Questions Solved = 45
Time Taken = 3 hours
Questions Solved = 75
Time Taken = 5 hours
To check whether the aspirant is solving questions at the same speed, we compare the ratio of questions solved to time taken.
Questions Solved : Time Taken
= 45 : 3
and
= 75 : 5
Using the ratio formula,
45/3
= 15
and
75/5
= 15
Since
45/3 = 75/5
Therefore,
45 : 3 = 75 : 5
Hence, the given ratios are in proportion.
Question 6: In a written Bank PO examination, the ratio of candidates who qualified to the total candidates who appeared was 39 : 65 in Centre A. In Centre B, the ratio of qualified candidates to total candidates who appeared was 6 : 10. Do these ratios form a proportion?
Answer
Given,
Ratio of qualified candidates to total candidates in Centre A
= 39 : 65
Ratio of qualified candidates to total candidates in Centre B
= 6 : 10
To determine whether these ratios form a proportion, let us simplify both ratios.
Centre A Ratio
= 39/65
= (39÷13)/(65÷13)
= 3/5
Centre B Ratio
= 6/10
= (6÷2)/(10÷2)
= 3/5
Since both ratios simplify to the same value,
39 : 65 = 6 : 10
Therefore, the given ratios form a proportion.
Question 7:
In an SSC mock test, the ratio of Mathematics questions to Reasoning questions is 4 : 7. If there are 21 Reasoning questions, find the number of Mathematics questions.
Answer
Given,
Ratio of Mathematics Questions to Reasoning Questions
= 4 : 7
Number of Reasoning Questions
= 21
Let the number of Mathematics questions be x.
Using the proportion,
4 : 7 = x : 21
Using the ratio formula,
4/7 = x/21
Cross-multiplying,
7x = 4 × 21
7x = 84
x = 84/7
x = 12
Therefore, the number of Mathematics questions is 12.
Q 8: If 12, 18, x and 45 are in proportion, find the value of x.
Answer
Given,
12, 18, x and 45 are in proportion.
Therefore,
12 : 18 = x : 45
Using the ratio formula,
12/18 = x/45
Cross-multiplying,
18x = 12 × 45
18x = 540
x = 540/18
x = 30
Verification:
12 : 18
= 2 : 3
and
30 : 45
= 2 : 3
Since both ratios are equal,
12 : 18 = 30 : 45
Hence, the numbers are in proportion.
Question 9: If 18 : x = 27 : 45, find the value of x.
Answer
Given,
18 : x = 27 : 45
Using the ratio formula,
18/x = 27/45
Cross-multiplying,
27x = 18 × 45
27x = 810
x = 810/27
x = 30
Therefore, x = 30.
Question 10: In Mukherjee Pur, the ratio of literate people to the total population is 42 : 70. In Shanti Nagar, the ratio of literate people to the total population is 54 : 90. Do these ratios form a proportion?
Answer
Given,
Ratio of Literate People to Total Population in Mukherjee Pur
= 42 : 70
Ratio of Literate People to Total Population in Shanti Nagar
= 54 : 90
To determine whether these ratios form a proportion, let us simplify both ratios.
Mukherjee Pur Ratio
= 42/70
= (42 ÷ 14)/(70 ÷ 14)
= 3/5
Shanti Nagar Ratio
= 54/90
= (54 ÷ 18)/(90 ÷ 18)
= 3/5
Since both ratios simplify to the same value,
42 : 70 = 54 : 90
Therefore, the given ratios form a proportion.
Question 11: A Canon imagePROGRAF TM-5250 printer prints 1,200 high-quality canvas prints in 3 hours. If it continues printing at the same rate, can it print 2,000 canvas prints in 5 hours?
Answer
Given,
Number of Canvas Prints = 1,200
Time Taken = 3 hours
Number of Canvas Prints = 2,000
Time Taken = 5 hours
To check whether the printer is working at the same printing rate, we compare the ratio of prints produced to the time taken.
Canvas Prints : Time
= 1,200 : 3
and
= 2,000 : 5
Using the ratio formula,
1200/3
= 400
and
2000/5
= 400
Since
1200/3 = 2000/5
Therefore,
1,200 : 3 = 2,000 : 5
Hence, the given ratios are in proportion.
This means the printer is producing canvas prints at the same rate in both situations.
FAQ:
1. What is a proportion?
A proportion is a statement that shows two ratios are equal.
For example,
2 : 8 = 12 : 48
2. What is the formula of proportion?
The formula of proportion is:
a : b :: c : d
or
a/b = c/d
If four numbers are in proportion, then
ad = bc
3. How do you check whether four numbers are in proportion?
Four numbers are in proportion if their corresponding ratios are equal.
For example,
2 : 4 and 12 : 24
2/4 = 1/2
12/24 = 1/2
Since both ratios are equal, the four numbers are in proportion.
You can also verify this using the rule:
ad = bc
4. What is the difference between ratio and proportion?
A ratio compares two quantities, whereas a proportion compares two ratios.
For example,
Ratio: 2 : 3
Proportion: 2 : 3 = 4 : 6
5. Can quantities with different units form a proportion?
Yes, but the quantities must first be converted into the same units before comparing the ratios.
For example,
24 cm : 4 m
First convert 4 m into 400 cm
or convert 24 cm into 0.24 m.
Then,
24 cm : 400 cm
= 3 : 50
Only after converting the quantities into the same units can the ratio be compared correctly.
6. How is proportion used in SSC and RRB exams?
Proportion is an important topic in SSC, RRB, Banking, NDA, CDS, Defence, CSAT, and other competitive examinations.
Questions are commonly asked on:
- Checking whether ratios are in proportion
- Finding a missing term
- Word problems based on proportion
- Direct and inverse proportion
Therefore, practicing proportion questions is important for scoring well in competitive exams.
Related Ratio and Proportion Resources
- 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
- 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)