This section covers basic ratio questions and answers to help you start applying the concepts of ratio and proportion.
For a complete understanding of the fundamentals, you can first go through our Ratio and Proportion section and Ratio Formula with Examples and Explanations page.
Once you complete these basic ratio questions and answers, you will develop a strong understanding of ratio concepts and their applications.
Question: 1
Find the ratio of the following:
(a) 45 minutes to 2 hours
Answer:
First convert both quantities into the same unit.
2 hours = 120 minutes (1 hour=60 minutes)
Ratio
= 45 : 120
HCF of 45 and 120 = 15
= (45/15) : (120/15)
= 3 : 8
Therefore, the required ratio is 3 : 8.
(b) 75 cm to 2.5 m
Answer:
First convert both quantities into the same unit.
2.5 m = 250 cm (1 meter =100 cm)
Ratio
= 75 : 250
HCF of 75 and 250 = 25
= (75/25) : (250/25)
= 3 : 10
Therefore, the required ratio is 3 : 10.
(c) ₹3 to 75 paise
Answer:
First convert both quantities into the same unit.
₹3 = 300 paise ( 1 rupees= 100 paise)
Ratio
= 300 : 75
HCF of 300 and 75 = 75
= (300/75) : (75/75)
= 4 : 1
Therefore, the required ratio is 4 : 1.
(d) 750 mL to 3 litres
Answer:
First convert both quantities into the same unit.
3 litres = 3000 mL
Ratio
= 750 : 3000
HCF of 750 and 3000 = 750
= (750/750) : (3000/750)
= 1 : 4
Therefore, the required ratio is 1 : 4.
Question 2:
A coaching institute has 200 female candidates and 150 male candidates enrolled for an SSC examination.
(a) Find the ratio of female candidates to male candidates.
(b) Find the ratio of female candidates to the total number of candidates enrolled.
Solution
A coaching institute has 200 female candidates and 150 male candidates enrolled for an SSC examination.
(a) Find the ratio of female candidates to male candidates.
Female Candidates : Male Candidates
= 200 : 150
HCF of 200 and 150 = 50
= (200/50) : (150/50)
= 4 : 3
Answer: The ratio of female candidates to male candidates is 4 : 3.
(b) Find the ratio of female candidates to the total number of candidates enrolled.
Total Candidates
= 200 + 150
= 350
Female Candidates : Total Candidates
= 200 : 350
HCF of 200 and 350 = 50
= (200/50) : (350/50)
= 4 : 7
Answer: The ratio of female candidates to the total number of candidates is 4 : 7.
Question 3:
At an RRB coaching centre, 120 candidates are enrolled. Out of them, 24 candidates prefer Quantitative Aptitude, 48 candidates prefer Reasoning, and the remaining candidates prefer General Science.
Find the ratio of:
(a) Number of candidates preferring Quantitative Aptitude to the number of candidates preferring General Science.
(b) Number of candidates preferring Reasoning to the total number of candidates enrolled.
Answer
Total Candidates = 120
Quantitative Aptitude = 24
Reasoning = 48
General Science = 120 − (24 + 48)
= 48
(a) Ratio of Quantitative Aptitude candidates to General Science candidates
= 24 : 48
=(24/24) : (48/24)
= 1 : 2
Answer: 1 : 2
(b) Ratio of Reasoning candidates to Total Candidates
= 48 : 120
= 2 : 5
Answer: 2 : 5
Question 4:
Two candidates are travelling to different RRB examination centres. One candidate covers 45 km in 1 hour, while the other covers 60 km in 1 hour.
Find the ratio of the speed of the first candidate to the speed of the second candidate.
Answer
Speed of First Candidate
= Distance Travelled / Time Taken
= 45/1
= 45 km/h
Speed of Second Candidate
= Distance Travelled / Time Taken
= 60/1
= 60 km/h
Ratio of Speeds
= 45 : 60
HCF of 45 and 60 = 15
= (45/15) : (60/15)
= 3 : 4
Therefore, the ratio of the speed of the first candidate to the speed of the second candidate is 3 : 4.
Question 5: A bank employee earns ₹6,00,000 per year. Out of this amount, he deposits ₹2,00,000 annually in his savings and investment accounts.
Find the ratio of:
(a) Annual income to annual savings.
(b) Annual savings to annual expenditure.
Answer
Annual Income = ₹6,00,000
Annual Savings = ₹2,00,000
(a) Ratio of Annual Income to Annual Savings
= 6,00,000 : 2,00,000
= 3 : 1
Answer: 3 : 1
(b) Ratio of Annual Savings to Annual Expenditure
Annual Expenditure
= ₹6,00,000 − ₹2,00,000
= ₹4,00,000
Savings : Expenditure
= 2,00,000 : 4,00,000
= 1 : 2
Answer: 1 : 2
Question 6:
Find the missing numbers so that all the ratios are equivalent:
15/18 = x/6 = 10/y = z/30
Answer:
15/18 = 5/6
Therefore,
x/6 = 5/6
x = 5
10/y = 5/6
5y = 60
y = 12
z/30 = 5/6
6z = 150
z = 25
Therefore,
15/18 = 5/6 = 10/12 = 25/30
Note: Equivalent Ratios:
Ratios that simplify to the same value are called equivalent ratios.
Question 7: A stationery shop sells 12 pens for ₹180 and 8 ball pens for ₹56. Find the ratio of the cost of one pen to the cost of one ball pen.
Answer
Cost of 12 pens = ₹180
Therefore,
Cost of 1 pen
= 180/12
= ₹15
Cost of 8 ball pens = ₹56
Therefore,
Cost of 1 ball pen
= 56/8
= ₹7
Ratio of Cost of One Pen to Cost of One Ball Pen
= 15 : 7
Therefore, the required ratio is 15 : 7.
Question 8:
Raj purchased 3 pens for ₹15, while Anu purchased 10 pens for ₹50. Whose pens are more expensive?
Answer
Cost of 1 pen purchased by Raj
= ₹15/3
= ₹5
Cost of 1 pen purchased by Anu
= ₹50/10
= ₹5
Ratio of Cost of One Pen Purchased by Raj to Cost of One Pen Purchased by Anu
= 5 : 5
= 1 : 1
Since the ratio is 1 : 1, the cost of one pen is the same for both Raj and Anu.
Therefore, neither Raj’s pens nor Anu’s pens are more expensive. Both purchased pens at the same price.
Question 9: Vendor A sells 15 kg of apples for ₹1,275, while Vendor B sells 18 kg of apples for ₹1,620. Compare the cost per kilogram and determine whose apples are more expensive.
Answer
Cost of 1 kg apples sold by Vendor A
= ₹1,275/15
= ₹85
Cost of 1 kg apples sold by Vendor B
= ₹1,620/18
= ₹90
Ratio of Cost of 1 kg Apples (Vendor A : Vendor B)
= 85 : 90
= (85/5) : (90/5)
= 17 : 18
Since ₹90 > ₹85, the cost of 1 kg apples sold by Vendor B is higher.
Therefore, the ratio of the cost of 1 kg of apples sold by Vendor A to Vendor B is 17 : 18, and Vendor B’s apples are more expensive.
Question 10: Divide ₹720 between Rahul and Mohit in the ratio 5 : 7.
Answer
Ratio of Rahul and Mohit
= 5 : 7
Total Parts
= 5 + 7
= 12
Value of One Part
= ₹720/12
= ₹60
Rahul’s Share
= 5 × ₹60
= ₹300
Mohit’s Share
= 7 × ₹60
= ₹420
Therefore, Rahul receives ₹300 and Mohit receives ₹420.
Question 11: The ratio of boys to girls in a banking coaching class is 5 : 4. If the number of boys in the class is 25, find the number of girls.
Answer
Ratio of Boys : Girls
= 5 : 4
Number of Boys = 25
Since 5 parts represent 25 boys,
Value of 1 Part
= 25/5
= 5
Number of Girls
= 4 × 5
= 20
Therefore, the number of girls in the coaching class is 20.
Important Resources to Ratio and Proportion
- Ratio and Proportion
- Ratio Formula with Examples and Explanations
- Ratio Word Problems with Answers
- Proportion Questions and Answers with Solutions
- 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)