📖 Introduction
Improve your quantitative aptitude with 10 tough Ratio and Proportion Questions with Answers (Questions 21–30) designed for Banking Mains preparation. This practice set covers continued proportion, combined ratios, mixture replacement, worker efficiency, income and expenditure, population growth, election statistics, business profits, inverse proportion and advanced partnership. Each question uses a different application of ratio and proportion and includes a concise shortcut method for faster exam calculations.
Table of Contents
📌 Question 21
📝 Question
Three positive numbers A, B and C are in continued proportion. Their sum is 210, while their product is 2,16,000. Find the ratio of the sum of the smallest and largest numbers to the middle number.
⚡ Shortcut Method
Since A, B and C are in continued proportion:
B² = AC
Therefore:
ABC = B³
B³ = 2,16,000
B = 60
A + B + C = 210
Therefore:
A + C = 210 − 60 = 150
Required ratio:
(A + C) : B = 150 : 60 = 5 : 2
✅ Final Answer
5 : 2
📌 Question 22
📝 Question
A banking company operates three regional training centres P, Q and R. The numbers of employees assigned to these centres are in the ratio 6 : 8 : 9. The average training hours required per employee at the three centres are in the ratio 5 : 6 : 8.
The company allocates its training budget in proportion to the total training hours required at each centre. If the total annual training budget is ₹4,40,000, find the amount allocated to Centre R.
⚡ Shortcut Method
Training requirement is proportional to:
Number of employees × Training hours per employee
P = 6 × 5 = 30
Q = 8 × 6 = 48
R = 9 × 8 = 72
Ratio:
30 : 48 : 72 = 5 : 8 : 12
Total parts = 25
R’s share:
4,40,000 × 12/25 = ₹2,11,200
= ₹2,11,200
✅ Final Answer
₹2,11,200
📌 Question 23
📝 Question
Three vessels contain milk-water mixtures as follows:
- Vessel A: 60 litres, milk : water = 5 : 3
- Vessel B: 90 litres, milk : water = 7 : 8
- Vessel C: 150 litres, milk : water = 9 : 11
The three mixtures are completely combined. Then 60 litres of the resulting mixture are removed and replaced with pure water.
Find the final ratio of milk to water.
⚡ Shortcut Method
Initial milk:
A = 60 × 5/8 = 37.5 L
B = 90 × 7/15 = 42 L
C = 150 × 9/20 = 67.5 L
Total milk = 147 L
Total mixture = 300 L
Total water = 153 L
60 L out of 300 L is removed, so 80% remains.
Milk remaining:
147 × 80% = 117.6 L
Water remaining:
153 × 80% = 122.4 L
Then 60 L pure water is added.
Final water:
122.4 + 60 = 182.4 L
Final ratio:
117.6 : 182.4
= 49 : 76
✅ Final Answer
49 : 76
📌 Question 24
📝 Question
The efficiencies of workers A, B and C are in the ratio 4 : 5 : 6.
A works for 24 days.
B works for 20 days, but during his final 8 working days his efficiency falls by 20%.
C works for 18 days, but during his final 6 working days his efficiency increases by 50%.
Find the ratio of the total work completed by A, B and C.
⚡ Shortcut Method
A:
4 × 24 = 96
B works 12 days at normal efficiency and 8 days at 80% efficiency:
5 × 12 + 5 × 80% × 8
= 60 + 32
= 92
C works 12 days normally and 6 days at 150% efficiency:
6 × 12 + 6 × 150% × 6
= 72 + 54
= 126
Ratio:
96 : 92 : 126
Divide by 2:
48 : 46 : 63
✅ Final Answer
48 : 46 : 63
📌 Question 25
📝 Question
The monthly incomes of A, B and C are in the ratio 9 : 12 : 16, while their monthly expenditures are in the ratio 5 : 7 : 10. Their savings are in the ratio 4 : 5 : 6.
If C saves ₹36,000 per month, find the combined monthly income of A, B and C.
⚡ Shortcut Method
Let’s verify the potentially tricky part.
Income ratio:
9 : 12 : 16
Expenditure ratio:
5 : 7 : 10
If the common scale is the same, savings become:
9 − 5 = 4
12 − 7 = 5
16 − 10 = 6
So savings ratio = 4 : 5 : 6, exactly as given.
C’s saving = ₹36,000.
6 parts = ₹36,000
1 part = ₹6,000
Total income:
(9 + 12 + 16) × 6,000
= 37 × 6,000
= ₹2,22,000
✅ Final Answer
₹2,22,000
📌 Question 26
📝 Question
The initial populations of towns A, B and C are in the ratio 7 : 9 : 12.
During one year, their populations increase by 20%, 10%, and 25%, respectively.
At the end of the year, ₹1,400 people migrate from C to A.
After migration, the populations of A and C are in the ratio 4 : 5.
Find the initial population of B.
⚡ Shortcut Method
Initial populations:
A = 7x
B = 9x
C = 12x
After growth:
A = 7x × 120% = 8.4x
C = 12x × 125% = 15x
After 1,400 people move from C to A:
A = 8.4x + 1,400
C = 15x − 1,400
Given A : C = 4 : 5:
(8.4x + 1,400) : (15x − 1,400) = 4 : 5
Solving gives:
x = 700
Therefore B:
9 × 700 = 6,300
✅ Final Answer
6,300
📌 Question 27
📝 Question
In an election, candidates A, B and C originally receive votes in the ratio 5 : 7 : 9.
The percentages of votes declared invalid for A, B and C are 8%, 10%, and 20%, respectively.
If the total number of valid votes is 3,62,000, find the difference between the number of valid votes received by B and C.
⚡ Shortcut Method
Valid votes:
A = 5x × 92% = 4.6x
B = 7x × 90% = 6.3x
C = 9x × 80% = 7.2x
Total valid votes:
4.6x + 6.3x + 7.2x = 18.1x
18.1x = 3,62,000
x = 20,000
Difference between B and C:
(7.2 − 6.3) × 20,000
= 0.9 × 20,000
= 18,000
✅ Final Answer
18,000 votes
📌 Question 28
📝 Question
Three business divisions A, B and C have gross sales in the ratio 6 : 8 : 11.
Their sales returns are 5%, 10%, and 8% of gross sales respectively.
The profit margins on their respective net sales are 12%, 15%, and 10%.
Find the ratio of the profits earned by A, B and C.
⚡ Shortcut Method
Net sales:
A = 6 × 95%
B = 8 × 90%
C = 11 × 92%
Profit:
A = 6 × 95% × 12%
B = 8 × 90% × 15%
C = 11 × 92% × 10%
Removing the common factor 1%:
684 : 1080 : 1012
Divide by 4:
171 : 270 : 253
✅ Final Answer
171 : 270 : 253
📌 Question 29
📝 Question
A factory uses 18 identical machines, working 15 hours per day for 8 days, to manufacture 7,200 units.
A new order requires 10,800 units to be produced in 12 days. Due to electricity restrictions, each machine can work only 10 hours per day.
Assuming all machines operate at the same efficiency, how many machines are required?
⚡ Shortcut Method
From the original situation:
18 machines × 15 hours × 8 days → 7,200 units
New requirement:
10,800 units in 12 days, with 10 hours/day.
Machines required:
18 × (10,800/7,200) × (15/12) × (8/10)
= 18 × 3/2 × 5/4 × 4/5
= 27 machines
✅ Final Answer
27 machines
📌 Question 30 👑 BrainQuro Grand Challenge
📝 Question
A company has three investment divisions A, B and C. Their initial investments are in the ratio 6 : 8 : 11.
After 4 months:
- A increases its investment by 50%.
- B reduces its investment by 25%.
- C makes no change.
After another 4 months:
- A withdraws 20% of its then-current investment.
- B restores its investment to the original level.
- C increases its investment by 20%.
During the final 4 months, all three investments remain unchanged.
The company earns a total annual profit of ₹9,92,500.
Find C’s share of the profit.
⚡ Shortcut Method
A’s investment-time
First 4 months:
6 × 4 = 24
Next 4 months:
6 × 150% = 9
9 × 4 = 36
Final 4 months:
9 × 80% = 7.2
7.2 × 4 = 28.8
Total:
24 + 36 + 28.8 = 88.8
B’s investment-time
First 4 months:
8 × 4 = 32
Next 4 months:
8 × 75% = 6
6 × 4 = 24
Final 4 months:
8 × 4 = 32
Total:
32 + 24 + 32 = 88
C’s investment-time
First 8 months:
11 × 8 = 88
Final 4 months:
11 × 120% = 13.2
13.2 × 4 = 52.8
Total:
88 + 52.8 = 140.8
Therefore profit ratio:
88.8 : 88 : 140.8
Multiply by 10:
888 : 880 : 1408
Divide by 8:
111 : 110 : 176
Total parts:
111 + 110 + 176 = 397
C’s share:
₹9,92,500 × 176/397
Since ₹9,92,500 ÷ 397 = ₹2,500:
₹2,500 × 176 = ₹4,40,000
✅ Final Answer
₹4,40,000
📚 Recommended Reading
- Profit and Loss Questions Series
- Percentage Questions with Answers
- Ratio and Proportion Questions with Answers| Part 1
- Ratio and Proportion Questions with Answers| Part 2
💡 Shortcut Trick of the Day
When a quantity changes over different periods, break the entire period into segments and calculate quantity × duration for every segment. Add the weighted contributions only after accounting for every change.
🎯 Challenge Question
The ratio of investments of A, B and C is 7 : 9 : 12. After 3 months, A increases his investment by 40%, B reduces it by 1/3, and C remains unchanged. After another 5 months, A withdraws 25% of his then-current investment, B restores his original investment, and C increases his investment by 50% for the remaining period.
Find the final profit-sharing ratio of A, B and C.
