Ratio and Proportion is an important topic in Banking Mains Quantitative Aptitude, especially when questions combine ratios with percentages, averages, work, expenditure, partnership, and algebraic conditions.
This practice set contains 10 hard Ratio and Proportion questions with answers, designed for candidates preparing for SBI PO, IBPS PO, and other banking exams. The questions in this set focus on multi-step calculations and different concepts rather than repeating the same question pattern.
Try each question yourself first, then use the shortcut answer to check your approach. The set covers Questions 41–50 of the BrainQuro Ratio and Proportion series.
Table of Contents
10 Hard Ratio and Proportion Questions with Answers for Banking Mains (41–50)
Question 41 🔥🔥🔥
📝 Question
A, B and C start a business with capitals in the ratio 4 : 5 : 6.
- After 3 months, A increases his capital by 25%.
- After 5 months, B withdraws 20% of his capital.
- After 7 months, C increases his capital by 25%.
If the total profit earned at the end of the year is ₹1,13,700, find the profit earned by C.
⚡ Shortcut Answer
Effective capital:
A = 4 × 3 + 5 × 9 = 57
B = 5 × 5 + 4 × 7 = 53
C = 6 × 7 + 7.5 × 5 = 79.5
Therefore:
57 : 53 : 79.5
Multiply by 2:
114 : 106 : 159
Total parts:
114 + 106 + 159 = 379
C’s profit:
₹1,13,700 × 159/379
= ₹47,700
✅ Final Answer
₹47,700
Question 42 🔥
📝 Question
A manufacturer purchases three raw materials P, Q and R in quantities in the ratio 4 : 5 : 6.
Their listed prices per unit are in the ratio 9 : 8 : 5. The manufacturer receives discounts of 20% on P, 25% on Q and 10% on R.
If the total amount paid is ₹14,300, find the amount paid for Q.
⚡ Shortcut Answer
Effective price ratio:
9 × 80% : 8 × 75% : 5 × 90%
= 7.2 : 6 : 4.5
Expenditure ratio:
4 × 7.2 : 5 × 6 : 6 × 4.5
= 28.8 : 30 : 27
= 48 : 50 : 45
Total parts = 143
Value of 1 part = 14,300 ÷ 143 = ₹100
Q’s expenditure:
50 × 100 = ₹5,000
✅ Final Answer
₹5,000
Question 43 🔥🔥
📝 Question
Four quantities A, B, C and D satisfy:
A : B = 2 : 3
B : C = 4 : 5
C : D = 6 : 7
A, B, C and D are then increased by 25%, 20%, 10% and 40%, respectively.
If the resulting total is ₹1,308, find the original value of C.
⚡ Shortcut Answer
First combine the ratios:
A : B : C : D
= 16 : 24 : 30 : 35
After the respective increases:
A : B : C : D
= 20 : 28.8 : 33 : 49
Multiplying by 5:
= 100 : 144 : 165 : 245
Total = 654 parts
1 part = 1,308 ÷ 654 = ₹2
Original C:
30 × 2 = ₹60
✅ Final Answer
₹60
Question 44 🔥🔥
📝 Question
A project is completed by 24 workers working for 15 days, 8 hours per day, at an efficiency represented by 5 units.
A second project requires 25% more work. For this project:
- efficiency is 25% lower,
- working hours are increased to 10 hours per day, and
- the project must be completed in 12 days.
Find the number of workers required for the second project.
⚡ Shortcut Answer
Workers ∝ Work / (Days × Hours × Efficiency)
New workers:
= 24 × 125% × 15/12 × 8/10 × 1/75%
= 24 × 5/4 × 5/4 × 4/5 × 4/3
= 40
✅ Final Answer
40 workers
You Might Also Like:-
- Hard ratio and proportion questions
- Ratio and proportion questions for banking exams
- Ratio and proportion questions for banking mains
- Previous Ratio and Proportion practice set
- Percentage questions for Banking Exams
- Banking-level Profit and Loss practice
Question 45 🔥🔥
📝 Question
Two positive numbers x and y satisfy:
(3x + 5y) : (3x − 5y) = 7 : 2
If x + y = 80, find the value of 4x + 7y.
⚡ Shortcut Answer
(3x + 5y)/(3x − 5y) = 7/2
Cross multiplication:
6x + 10y = 21x − 35y
45y = 15x
Therefore:
x : y = 3 : 1
x + y = 80
3 parts = 80
x = 60, y = 20
Therefore:
4x + 7y
= 4(60) + 7(20)
= 380
✅ Final Answer
380
Question 46🔥
📝 Question
The numbers of students in three batches A, B and C are in the ratio 5 : 7 : 9.
The average marks of the students in these batches are in the ratio 6 : 5 : 4.
If the average marks of A increase by 25%, those of B decrease by 10%, and those of C increase by 20%, find the ratio of the new total marks of A, B and C.
⚡ Shortcut Answer
Total marks ∝ Number of students × Average marks.
New total-mark ratio:
A : B : C
= 5 × 6 × 125% : 7 × 5 × 90% : 9 × 4 × 120%
= 37.5 : 31.5 : 43.2
Multiplying by 10:
375 : 315 : 432
= 125 : 105 : 144
✅ Final Answer
125 : 105 : 144
Question 47 🔥🔥
📝 Question
A sum is divided among A, B and C in the ratio 4 : 5 : 6.
A transfers 25% of his share to B. B then transfers 20% of his resulting share to C.
If C’s final share is ₹5,400, find A’s original share.
⚡ Shortcut Answer
Original:
A = 4x
B = 5x
C = 6x
A transfers 25% of 4x = x to B.
So B becomes 6x.
B transfers 20% of 6x = 1.2x to C.
Therefore C becomes:
6x + 1.2x = 7.2x
Given:
7.2x = 5,400
x = 750
A’s original share:
4 × 750 = ₹3,000
✅ Final Answer
₹3,000
Question 48 🔥🔥
📝 Question
The prices of three machines A, B and C are in the ratio 5 : 7 : 9, while their numbers of units sold are in the ratio 9 : 8 : 5.
Discounts of 20%, 25% and 10% are offered on A, B and C respectively.
If the total revenue after discounts is ₹47,400, find the revenue generated by B.
⚡ Shortcut Answer
Revenue ratio:
A : B : C
= 5 × 9 × 80% : 7 × 8 × 75% : 9 × 5 × 90%
= 36 : 42 : 40.5
= 72 : 84 : 81
Total parts = 237
1 part = 47,400 ÷ 237 = ₹200
B’s revenue:
84 × 200 = ₹16,800
✅ Final Answer
₹16,800
Question 49 🔥🔥🔥
📝 Question
A, B and C have monthly incomes in the ratio 7 : 9 : 12. Their monthly expenditures are in the ratio 5 : 7 : 10.
A saves ₹8,000 per month, while B saves ₹10,000 per month.
If C’s income is increased by 20% and his expenditure is increased by 10%, find C’s new monthly savings.
⚡ Shortcut Answer
Let the common factors for income and expenditure be x and y.
Step 1: Use A’s savings
Income of A = 7x
Expenditure of A = 5y
So:
7x − 5y = 8,000 …(1)
Step 2: Use B’s savings
Income of B = 9x
Expenditure of B = 7y
So:
9x − 7y = 10,000 …(2)
Multiply (1) by 7:
49x − 35y = 56,000
Multiply (2) by 5:
45x − 35y = 50,000
Subtract:
4x = 6,000
Therefore:
x = 1,500
From (1):
7(1,500) − 5y = 8,000
10,500 − 5y = 8,000
5y = 2,500
y = 500
Step 3: Find C’s original income and expenditure
C’s income:
12x = 12 × 1,500 = ₹18,000
C’s expenditure:
10y = 10 × 500 = ₹5,000
So C’s original savings = ₹13,000.
Step 4: Apply the changes
C’s income increases by 20%:
₹18,000 × 120% = ₹21,600
C’s expenditure increases by 10%:
₹5,000 × 110% = ₹5,500
Therefore, new savings:
₹21,600 − ₹5,500 = ₹16,100
✅ Final Answer: ₹16,100
✅ Final Answer
₹16,100
Question 50 🔥🔥🔥
📝 Question
Two positive numbers A and B satisfy the condition:
(5A + 3B) : (3A + 5B) = 13 : 11
If A + B = 192, find the value of 2A + 3B.
⚡ Shortcut Answer
(5A + 3B)/(3A + 5B) = 13/11
Cross multiplication:
55A + 33B = 39A + 65B
16A = 32B
Therefore:
A : B = 2 : 1
A + B = 192
3 parts = 192
A = 128
B = 64
Therefore:
2A + 3B
= 2(128) + 3(64)
= 256 + 192
= 448
✅ Final Answer
448
🔥 BrainQuro Extreme Challenge Question
📝 Challenge Question
The monthly incomes of A, B and C are in the ratio 8 : 11 : 14, while their monthly expenditures are in the ratio 5 : 7 : 9.
A’s monthly saving is ₹6,800.
Now, A’s income is increased by 15% and his expenditure by 10%. At the same time, B’s income is increased by 20% and his expenditure by 25%.
C’s income is increased by 20%, while his expenditure is increased by 10%.
After these changes, C’s new monthly saving is exactly twice B’s original monthly saving, and C’s new saving exceeds A’s original saving by ₹10,600.
Find the original monthly income of C.
Give Your Answer in Comments
⚡ Shortcut Trick of the Day
When income and expenditure are given in ratios, and savings are provided, avoid finding every actual value immediately.
Use this structure:
Income = Ratio × x
Expenditure = Ratio × y
Then directly form:
Income − Expenditure = Saving
For the challenge question:
A’s saving:
8x − 5y = 6,800
B’s original saving can be obtained directly from the given condition:
C’s new saving = 2 × B’s saving
and
C’s new saving = 6,800 + 10,600 = 17,400
Therefore:
B’s saving = 17,400 ÷ 2 = 8,700
Now:
11x − 7y = 8,700
So we only need to solve:
8x − 5y = 6,800
11x − 7y = 8,700
Eliminating y gives:
x = 4,100
Hence C’s income:
14 × 4,100 = ₹57,400
🧠 Banking Mains Tip
Whenever you see Income Ratio + Expenditure Ratio + Savings, immediately introduce two variables (x and y) instead of assigning an actual income. This usually turns a lengthy-looking question into two linear equations, which can be solved much faster.
