📖 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
Time-weighted investments
A = 8×5 + 6×7 = 82
B = 10×5 + 12×7 = 134
C = 15×12 = 180
Ratio = 82 : 134 : 180
B’s Share
= 990000 × 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
=(7/10 + 9/14)/2
=(49+45)/70
=47/70
Total
=96 ×70/47
≈143 litres
✅ Final Answer
143 litres (approximately)
📌 Question 3
📝 Question
The monthly salaries of P, Q, R and S are in the ratio 5 : 7 : 9 : 11. Their monthly expenditures are in the ratio 4 : 5 : 8 : 9, and each saves ₹18,000 per month. Find the monthly salary of S.
⚡ Shortcut Method
Let common factors be x and y.
5x−4y
=7x−5y
=9x−8y
=11x−9y
=18000
⇒ x=9000
Salary of S
=11×9000
=₹99,000
✅ Final Answer
₹99,000
📌 Question 4
📝 Question
The number of boys and girls in School A is 11 : 9, while in School B it is 7 : 5. If both schools are merged and the overall ratio becomes 25 : 21, find the ratio of total students in School A to School B.
⚡ Shortcut Method
Let totals be A and B.
11/20 A +7/12 B
25/46(A+B)
Solve
A:B
=35:48
✅ Final Answer
35 : 48
📌 Question 5
📝 Question
A chemical solution contains Acid, Water and Alcohol in the ratio 5 : 8 : 7. After removing 20% of the solution and replacing it entirely with alcohol, the new ratio becomes 4 : 6 : 10. Find the initial quantity of the solution.
⚡ Shortcut Method
Initial alcohol
=7/20 T
Final alcohol
=7/20×0.8T+0.2T
=12/25T
Given ratio
10/20=1/2
T=200 litres
✅ Final Answer
200 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
Actual production
9×22
12×25
15×28
=198:300:420
=33:50:70
✅ Final Answer
33 : 50 : 70
📌 Question 7
📝 Question
The ages of A, B and C are in the ratio 5 : 7 : 9. Eight years ago, the ratio of A and B was 7 : 10. Find the present age of C.
⚡ Shortcut Method
5x−8
7x−8
=7:10
50x−80
49x−56
x=24
Age of C
=9×24
=216 years
✅ Final Answer
216 years
📌 Question 8
📝 Question
A contractor distributes wages among Skilled, Semi-skilled and Unskilled workers in the ratio 8 : 5 : 3. If the number of workers is in the ratio 3 : 5 : 8, find the ratio of total wages paid to each category.
⚡ Shortcut Method
Multiply
8×3
5×5
3×8
=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
Good products
7×98
9×97
11×95
=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
6×4
8×3
10×2
12×1
=20:24:24:20:12
=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.
