📖 Introduction
Ratio and Proportion is one of the most important topics in Banking Mains examinations because it frequently appears in lengthy business, partnership, mixture, production, and logical comparison problems. This practice set is specially designed for IBPS PO, SBI PO, RBI Assistant, LIC AAO, NIACL AO, SSC CGL, RRB NTPC, and other competitive exams.
Unlike basic ratio questions, every question in this series is Banking Mains level, requiring logical thinking, multiple-step calculations, and careful interpretation. Each shortcut method is kept concise to match the speed required in competitive exams.
Table of Contents
📌 Question 1
📝 Question
Three partners A, B and C invested money in a business in the ratio 8 : 10 : 15. After 5 months, A withdrew 25% of his investment, while B increased his investment by 20%. C kept his investment unchanged throughout the year. If the total profit at the end of the year is ₹9,90,000, then find B’s share of the profit.
⚡ Shortcut Method
A:
8 × 5 + 6 × 7 = 82
B:
10 × 5 + 12 × 7 = 134
C:
15 × 12 = 180
Profit ratio:
82 : 134 : 180
Total = 396 parts.
B’s share:
₹9,90,000 × 134/396 = ₹3,35,000
✅ Final Answer
₹3,35,000
📌 Question 2
📝 Question
The ratio of milk to water in Vessel A is 7 : 3, while in Vessel B it is 9 : 5. Equal quantities are taken from both vessels and mixed. If the final mixture contains 96 litres of milk, find the total quantity of the final mixture.
⚡ Shortcut Method
Milk fraction in A:
7/10
Milk fraction in B:
9/14
Since equal quantities are mixed, final milk fraction is:
(7/10 + 9/14) ÷ 2
= 47/70
Given milk = 96 litres.
Total mixture:
96 × 70/47
= 6720/47
= 142.98 litres approximately
✅ Final Answer
= 142.98 litres approximately
📌 Question 3 – Income, Expenditure & Savings
📝 Question
The monthly salaries of A, B, and C are in the ratio 8 : 11 : 14, while their monthly expenditures are in the ratio 5 : 7 : 9. If each person saves ₹27,000 per month, find the monthly salary of C.
⚡ Shortcut Method
Let salaries be:
8x, 11x, 14x
Let expenditures be:
5y, 7y, 9y
Since each saves the same amount:
8x − 5y = 11x − 7y
Therefore:
2y = 3x
So, y = 3x/2
C’s saving:
14x − 9y
= 14x − 9 × 3x/2
= 14x − 13.5x
= 0.5x
Given saving = ₹27,000:
0.5x = ₹27,000
x = ₹54,000
C’s salary:
14 × ₹54,000
= ₹7,56,000
✅ Final Answer
₹7,56,000
📌 Question 4 — Combined Ratio
📝 Question
The number of boys and girls in School A is in the ratio 11 : 9, while in School B it is 7 : 5. After the two schools are merged, the overall ratio of boys to girls becomes 25 : 19. Find the ratio of the total number of students in School A to that in School B.
⚡ Shortcut Method
Boys percentage in School A:
11/20
Boys percentage in School B:
7/12
Overall boys percentage:
25/44
Let total students in School A and B be A and B.
Then:
11/20 × A + 7/12 × B = 25/44 × (A + B)
Solving:
A : B = 5 : 6
✅ Final Answer
5 : 6
📌 Question 5 — Mixture Replacement
📝 Question
A chemical solution contains acid, water, and alcohol in the ratio 5 : 8 : 7. If 20% of the solution is removed and replaced entirely with pure alcohol, the new ratio of acid, water, and alcohol becomes 5 : 8 : 12. If the final quantity of alcohol is 60 litres, find the initial quantity of the solution.
⚡ Shortcut Method
Initially, alcohol = 7/20 of the solution.
After removing 20%, 80% of the original alcohol remains.
Alcohol remaining = 7/20 × 80% = 28/100 of the original quantity.
Pure alcohol added = 20% = 20/100.
Therefore, final alcohol = 48/100 = 12/25 of the initial quantity.
Given final alcohol = 60 litres:
Initial quantity = 60 × 25/12
= 125 litres
✅ Final Answer
125 litres
📌 Question 6
📝 Question
The production capacities of Machines A, B and C are in the ratio 9 : 12 : 15. Due to maintenance, A remains idle for 8 days, B for 5 days and C for 2 days during a 30-day month. Find the ratio of their actual monthly production.
⚡ Shortcut Method
A works:
30 − 8 = 22 days
Production = 9 × 22 = 198
B works:
30 − 5 = 25 days
Production = 12 × 25 = 300
C works:
30 − 2 = 28 days
Production = 15 × 28 = 420
Ratio:
198 : 300 : 420
Divide by 6:
33 : 50 : 70
✅ Final Answer
33 : 50 : 70
📌 Question 7 — Age Ratio
📝 Question
The present ages of A, B, and C are in the ratio 4 : 5 : 7. Six years ago, the ratio of the ages of A and B was 3 : 4. Find the present age of C.
⚡ Shortcut Method
Let present ages be:
A = 4x
B = 5x
C = 7x
Six years ago:
A = 4x − 6
B = 5x − 6
Given:
(4x − 6) : (5x − 6) = 3 : 4
Therefore:
4(4x − 6) = 3(5x − 6)
16x − 24 = 15x − 18
x = 6
Present age of C:
7 × 6 = 42 years
✅ Final Answer
42 years
📌 Question 8
📝 Question
A contractor pays the Skilled, Semi-skilled and Unskilled workers at wage rates in the ratio 8 : 5 : 3. If the number of workers is in the ratio 3 : 5 : 8, find the ratio of the total wages paid to each category.
⚡ Shortcut Method
Then:
Skilled = 8 × 3 = 24
Semi-skilled = 5 × 5 = 25
Unskilled = 3 × 8 = 24
Answer:
24 : 25 : 24
✅ Final Answer
24 : 25 : 24
📌 Question 9
📝 Question
Three companies X, Y and Z manufacture laptops in the ratio 7 : 9 : 11. Their defective products are in the ratio 2% : 3% : 5% respectively. Find the ratio of non-defective laptops produced.
⚡ Shortcut Method
Production ratio:
7 : 9 : 11
Non-defective percentages:
98%, 97%, 95%
Therefore:
7 × 98 = 686
9 × 97 = 873
11 × 95 = 1045
Ratio:
686 : 873 : 1045
✅ Final Answer
686 : 873 : 1045
📌 Question 10
📝 Question
Five departments contribute to a corporate project in the ratio 4 : 6 : 8 : 10 : 12. Their efficiencies are respectively proportional to 5 : 4 : 3 : 2 : 1. If the project output is shared in proportion to effective contribution, find the ratio of output shares.
⚡ Shortcut Method
Effective contribution:
4 × 5 = 20
6 × 4 = 24
8 × 3 = 24
10 × 2 = 20
12 × 1 = 12
Ratio:
20 : 24 : 24 : 20 : 12
Divide by 4:
5 : 6 : 6 : 5 : 3
✅ Final Answer
5 : 6 : 6 : 5 : 3
📚 Recommended Reading
- Profit and Loss Questions Series
- Percentage Questions with Answers
- Ratio and Proportion Questions with Answers| Part 2
💡 Shortcut Trick of the Day
For partnership problems, always convert changing investments into Investment × Time before comparing ratios. This avoids lengthy calculations and is the fastest approach in Banking exams.
🎯 Challenge Question
Three partners invest in the ratio 7 : 11 : 13. After four months, the first partner doubles his investment, the second withdraws one-third of his investment, and the third remains unchanged. Determine the final profit-sharing ratio after one year.
⚠️ Common Mistakes
- Ignoring the time factor in partnership questions.
- Using simple ratios instead of weighted ratios.
- Forgetting to account for efficiency when contributions differ.
- Mixing production ratio with output ratio.
- Reducing ratios before completing all calculations.
🚀 Banking Exam Speed Tips
- Convert ratios into fractions early.
- Use weighted averages for mixture questions.
- Multiply instead of converting to percentages repeatedly.
- Reduce ratios only at the final step.
- Check whether the question asks for quantity, ratio, or share before solving.
❓ FAQ
1. Are these questions suitable for SBI PO Mains?
Yes. This series is designed to progress toward SBI PO Mains level, with every question in this part already targeting a high level of reasoning.
2. Are all questions original?
Yes. Every question is uniquely created and not copied from books or websites.
3. Which exams can benefit from this series?
IBPS PO, SBI PO, IBPS Clerk, RBI Assistant, LIC AAO, SSC CGL, SSC CHSL, RRB NTPC, State PCS, and other competitive exams.
4. Do these questions include detailed solutions?
No. Only concise, exam-oriented shortcut methods are provided to improve speed.
5. How should I practice?
Attempt each question within 2–3 minutes, then compare your approach with the shortcut method.
