Can you solve a Ratio and Proportion question when the ratio is hidden inside a real-world situation? If you are preparing for SBI PO, IBPS PO, RBI Assistant, LIC AAO, SSC CGL, RRB NTPC, or other competitive exams, this practice set is designed to take your quantitative aptitude beyond basic ratio calculations.
Welcome to Part 4 of BrainQuro’s Ratio and Proportion Questions with Answers series, featuring 10 tough and original Banking Mains-level questions. If you are starting the series, you can first practice Ratio and Proportion Questions with Answers – Part 1, followed by Part 2 and Part 3 before attempting this advanced set.
This part moves beyond simple ratio simplification and tests how effectively you can apply ratios to mixtures, income and expenditure, coin values, population changes, alloys, work efficiency, student distribution, business data, and multi-stage quantity adjustments.
What makes these Ratio and Proportion Questions with Answers different is the variety of concepts and hidden relationships. Several questions require you to connect multiple conditions before arriving at the required ratio, closely matching the analytical thinking expected in difficult Banking Mains Quantitative Aptitude sections.
Try all 10 questions without looking at the shortcut methods first. Then use the concise exam-oriented calculations to identify faster approaches, verify your answers, and improve your calculation speed.
Build your basics. Master advanced ratios. Think beyond formulas. — BrainQuro.
Table of Contents
Ratio and Proportion Questions with Answers | Questions 31–40
📌 Question 31
📝 Question
A vessel contains a mixture of acid and water in the ratio 5 : 3. When 24 litres of the mixture is replaced with pure acid, the ratio of acid to water becomes 3 : 1. Again, 16 litres of the new mixture is removed and replaced with 12 litres of pure water. Find the final quantity of acid in the vessel.
⚡ Shortcut Method
Let initial quantity = x litres.
After first replacement:
Acid = 5x/8
Water = 3x/8 − 24
Given:
(5x/8) : (3x/8 − 24) = 3 : 1
5x/8 = 9x/8 − 72
x = 144 L
Initial acid = 90 L
After removing 16 L:
Acid removed = 90×16/144 = 10 L
Final acid = 90 − 10
= 80 L
✅ Final Answer
80 litres
📌 Question 32
📝 Question
The incomes of A, B and C are in the ratio 3 : 4 : 5, while their expenditures are in the ratio 4 : 5 : 6. If A saves 25% of his income, find the ratio of the savings of A, B and C.
⚡ Shortcut Method
Let incomes = 3x, 4x, 5x
A’s saving = 25% of 3x = 3x/4
A’s expenditure = 3x − 3x/4 = 9x/4
Since expenditure ratio = 4 : 5 : 6:
1 expenditure unit = 9x/16
Savings:
A = 3x/4 = 12x/16
B = 4x − 45x/16 = 19x/16
C = 5x − 54x/16 = 26x/16
Ratio
= 12 : 19 : 26
✅ Final Answer
12 : 19 : 26
📌 Question 33
📝 Question
A bag contains 1-rupee, 50-paise and 25-paise coins in the ratio 5 : 7 : 9. The total value of the coins is ₹430.
Now 20 one-rupee coins and 40 fifty-paise coins are added, along with some 25-paise coins. The ratio of the new total values of 1-rupee coins, 50-paise coins and 25-paise coins becomes 11 : 8 : 12.
Find the number of 25-paise coins added.
⚡ Shortcut Method
Let numbers initially be:
5x, 7x, 9x
Value:
5x + 3.5x + 2.25x = 430
10.75x = 430
x = 40
Initial values:
1-rupee = ₹200
50-paise = ₹140
25-paise = ₹90
After additions:
1-rupee = 200 + 20 = ₹220
50-paise = 140 + 20 = ₹160
220 : 160 = 11 : 8
Therefore 12 parts = ₹240
Additional 25-paise value:
= 240 − 90
= ₹150
Number added:
= 150/0.25
= 600
✅ Final Answer
600 coins
📌 Question 34
📝 Question
Two vessels A and B contain spirit and water in the ratios 5 : 2 and 7 : 6, respectively. To obtain a mixture containing spirit and water in the ratio 8 : 5, the quantities actually taken from A and B must be in a certain ratio.
If the quantity taken from A is one-fourth of the quantity in A and the quantity taken from B is one-third of the quantity in B, determine the ratio of the original quantities present in vessels A and B.
⚡ Shortcut Method
Let quantities actually mixed = x : y.
Spirit:
5x/7 + 7y/13
Water:
2x/7 + 6y/13
Given spirit : water = 8 : 5
Solving:
x : y = 7 : 9
But:
x = A/4
y = B/3
Therefore:
A/4 : B/3 = 7 : 9
A : B = 28 : 27
✅ Final Answer
28 : 27
📌 Question 35
📝 Question
The ratio of boys to girls in a college in 2024 was 12 : 11. In 2025, the number of boys increased by 20%, while the number of girls increased by x%. The ratio of boys to girls became 9 : 10.
If the total number of students in 2025 was 1,520, find the percentage increase in the number of girls.
⚡ Shortcut Method
2025 ratio = 9 : 10
Total = 1,520
Boys = 720
Girls = 800
Boys increased by 20%.
2024 boys
= 720/1.2
= 600
Since 2024 boys : girls = 12 : 11:
2024 girls
= 600×11/12
= 550
Increase in girls
= 800 − 550
= 250
Percentage increase
= 250/550 × 100
= 45.45%
✅ Final Answer
45.45% approximately
📌 Question 36
📝 Question
A sum of money is divided among P, Q, R and S such that:
- P’s share is 3/7 of the combined share of Q, R and S.
- Q’s share is 2/9 of the combined share of P, R and S.
- R’s share is 1/3 of the combined share of P, Q and S.
If the difference between P’s share and Q’s share is ₹5,200, find the total amount distributed.
⚡ Shortcut Method
Let total = T.
P = 3/10 T
Q = 2/11 T
Difference:
3T/10 − 2T/11
= (33T − 20T)/110
= 13T/110
Given:
13T/110 = 5,200
T = 5,200 × 110/13
= ₹44,000
✅ Final Answer
₹44,000
📌 Question 37
📝 Question
Three alloys A, B and C contain only gold, silver and copper.
- In alloy A, gold : silver = 2 : 3, with no copper.
- In alloy B, silver : copper = 4 : 5, with no gold.
- In alloy C, gold : copper = 5 : 6, with no silver.
Equal quantities of A and B are melted together to form alloy D. Alloy D and alloy C are then mixed in the ratio 3 : 4.
Find the ratio of gold to copper in the final mixture.
⚡ Shortcut Method
In equal quantities of A and B:
Gold in D = 1/5
Copper in D = 5/18
In C:
Gold = 5/11
Copper = 6/11
Final gold:
3×1/5 + 4×5/11
= 133/55
Final copper:
3×5/18 + 4×6/11
= 199/66
Ratio:
133/55 : 199/66
= 798 : 995
✅ Final Answer
798 : 995
📌 Question 38
📝 Question
The working efficiencies of A, B and C are in the ratio 2 : 3 : 5. They undertake a project for a total remuneration of ₹62,000.
A, B and C work together for the first 4 days. A then leaves. B and C continue for another 3 days, after which B’s efficiency drops by 50% for the remaining period. The project is completed in 10 days.
If the remuneration is distributed in proportion to each person’s actual contribution to the project, find the ratio in which the remuneration should be divided.
⚡ Shortcut Method
A’s contribution:
2×4 = 8
B’s contribution:
3×7 + 1.5×3
= 25.5
C’s contribution:
5×10 = 50
Ratio:
8 : 25.5 : 50
Multiply by 2:
= 16 : 51 : 100
✅ Final Answer
16 : 51 : 100
📌 Question 39
📝 Question
In a school, the numbers of students in Classes IX, X and XI are in the ratio 4 : 5 : 6.
For a district sports meet, 15% of Class IX, 20% of Class X and 25% of Class XI students are selected.
The ratio of the remaining students becomes 17 : 20 : y.
If 30 new students subsequently join Class XI, the final ratio of students in Class X to Class XI becomes 4 : 5.
Find y.
⚡ Shortcut Method
Remaining students:
IX = 4×85% = 3.4
X = 5×80% = 4
XI = 6×75% = 4.5
Ratio:
3.4 : 4 : 4.5
Multiply by 10:
= 34 : 40 : 45
Therefore:
y = 45
Check second condition:
Let common factor = 6.
X = 240
XI = 270
After 30 join XI:
XI = 300
X : XI = 240 : 300
= 4 : 5 ✓
✅ Final Answer
45
📌 Question 40 👑 BrainQuro Grand Challenge
📝 Question
AA retail company stores a particular product in three regional warehouses P, Q and R. Initially, the quantities stored in P, Q and R are in the ratio 6 : 8 : 11.
During a stock-restructuring exercise:
- Warehouse P dispatches 25% of its initial stock and then receives a quantity equal to 20% of its remaining stock.
- Warehouse Q dispatches 20% of its initial stock and subsequently receives a quantity equal to 25% of its initial stock.
- Warehouse R dispatches 30% of its initial stock and subsequently receives a quantity equal to 1/7 of its remaining stock.
After all these adjustments, the ratio of the stocks in P, Q and R becomes 27 : 42 : 44.
If the combined stock in the three warehouses after all adjustments is 22,600 units, find the initial stock of Warehouse R.
⚡ Shortcut Method
Let initial stocks:
P = 6x
Q = 8x
R = 11x
Final P:
= 6x × 75% × 120%
= 5.4x
Final Q:
= 8x × 80% + 8x × 25%
= 8.4x
Final R:
= 11x × 70% × 8/7
= 8.8x
Therefore final ratio:
5.4 : 8.4 : 8.8
= 27 : 42 : 44
Total parts:
27 + 42 + 44 = 113
113 parts = 22,600
1 part = 200
Final R = 44 × 200 = 8,800
Since final R = 8.8x:
8.8x = 8,800
x = 1,000
Initial R
= 11x
= 11,000
✅ Final Answer
11,000 units
🔗 Related Posts
- Ratio and Proportion Questions Part 1
- Ratio and Proportion Questions Part 2
- Ratio and Proportion Questions Part 3
- Ratio and Proportion Questions Part 5 (Coming Soon)
- Percentage Questions with Answers
- Profit and Loss Questions with Answers
💡 Shortcut Trick of the Day
When quantities change at different points in time, divide the timeline into separate periods and calculate effective quantity × duration for every period. This is especially useful in partnership, capital allocation and efficiency-based ratio problems.
🎯 Challenge Question
Three partners A, B and C invest in the ratio 4 : 7 : 9. After 3 months, A increases his investment by 50%, B withdraws 20%, and C remains unchanged. After another 4 months, A withdraws one-third of his then-current investment, B restores his original investment, and C increases his investment by 25% for the remaining period.
If the total profit is ₹8,52,000, determine the profit-sharing ratio and C’s share.
⚠️ Common Mistakes
- Forgetting that mixture is removed proportionally.
- Applying percentage changes to the wrong base.
- Combining ratios without equalising the common term.
- Confusing original quantities with final quantities.
- Ignoring time while calculating actual contribution.
- Applying profit margins directly to gross sales.
- Rounding intermediate calculations unnecessarily.
🚀 Banking Exam Speed Tips
- Convert ratio data into a common variable immediately.
- For mixtures, calculate component quantities before replacement.
- In income-expenditure problems, use one common income and expenditure unit.
- For workforce questions, use efficiency × time.
- For elections and student populations, separate original and remaining populations.
- For partnership and capital questions, use capital × duration.
- Keep fractions exact until the final calculation.
❓ FAQ
1. Are these Ratio and Proportion questions suitable for SBI PO Mains?
Yes. The set focuses on difficult applications of ratio and proportion rather than basic ratio simplification.
2. Which exams are covered by this practice set?
These questions are useful for SBI PO, IBPS PO, IBPS Clerk, RBI Assistant, LIC AAO, NIACL AO, UIIC AO, SSC CGL, SSC CHSL, RRB NTPC, State PCS and other competitive exams.
3. Are detailed solutions provided?
No. The series intentionally uses concise shortcut calculations to help aspirants develop faster exam-solving techniques.
4. How should I attempt these questions?
Try solving each question independently first. Give yourself approximately 2–4 minutes per question before checking the shortcut method and final answer.
