✍️ Introduction
Preparing for Banking and SSC exams? This practice set features 10 original Ratio and Proportion Questions with Answers (Questions 11–20) designed specifically for Banking Mains aspirants. The questions cover advanced concepts such as partnership, mixtures, age ratios, income and expenditure, worker efficiency, production, population growth, business profit sharing, combined ratios, and multi-concept reasoning. Each question includes a concise shortcut method and a verified final answer to help you improve both speed and accuracy for competitive exams like SBI PO, IBPS PO, RBI Assistant, LIC AAO, SSC CGL, and RRB NTPC.
Table of Contents
📌 Question 11 – Advanced Partnership
📝 Question
Three partners A, B, and C started a business by investing in the ratio 8 : 10 : 15.
After 4 months:
- A increased his investment by 25%.
- B withdrew 20% of his investment.
- C kept his investment unchanged.
After another 4 months:
- A made no further changes.
- B restored his investment to the original amount.
- C increased his investment by 20% for the remaining period.
If the total profit at the end of the year was ₹15,60,000, find A’s share of the profit.
⚡ Shortcut Method
A’s weighted investment:
8 × 4 + 10 × 8 = 112
B:
10 × 4 + 8 × 4 + 10 × 4 = 112
C:
15 × 8 + 18 × 4 = 192
Ratio:
112 : 112 : 192 = 7 : 7 : 12
Total parts = 26
A’s share:
₹15,60,000 × 7/26 = ₹4,20,000
✅ Final Answer
₹4,20,000
📌 Question 12 – Milk & Water
📝 Question
Container A contains 72 litres of a milk-water mixture in the ratio 7 : 2.
Container B contains 108 litres of another mixture in the ratio 5 : 4.
Both mixtures are poured into a third container. Then 36 litres of the resulting mixture are removed and replaced with pure milk.
Find the final ratio of milk to water.
⚡ Shortcut Method
Initial milk:
72 × 7/9 = 56 L
108 × 5/9 = 60 L
Total milk = 116 L.
Initial water = 16 + 48 = 64 L.
When 36 L out of 180 L is removed, 20% of each component is removed.
Milk remaining = 116 × 80% = 92.8 L
Water remaining = 64 × 80% = 51.2 L
Add 36 L pure milk:
Milk = 128.8 L
Water = 51.2 L
Ratio:
128.8 : 51.2
= 161 : 64
✅ Final Answer
161 : 64
📌 Question 13 – Age Ratio
📝 Question
The present ages of A, B, and C are in the ratio 9 : 13 : 16.
Eight years ago, the ratio of A and B was 7 : 11.
If five years from now the ratio of B and C is 19 : 23, find the present age of C.
⚡ Shortcut Method
Present ages:
A = 9x
B = 13x
C = 16x
Eight years ago:
(9x − 8) : (13x − 8) = 7 : 11
So:
11(9x − 8) = 7(13x − 8)
99x − 88 = 91x − 56
8x = 32
x = 4
C = 16 × 4 = 64 years
Check after 5 years:
B = 57
C = 69
57 : 69 = 19 : 23
✅ Final Answer
64 years
📌 Question 14 – Income, Expenditure & Savings
📝 Question
The monthly incomes of A, B, and C are in the ratio 12 : 15 : 20.
Their expenditures are in the ratio 7 : 9 : 11.
If their respective savings are in the ratio 22 : 27 : 38, find the ratio of the common expenditure unit to the common income unit.
⚡ Shortcut Method
Take:
Income = 12x : 15x : 20x
Expenditure = 7y : 9y : 11y
If x = 3 and y = 2:
A saving = 36 − 14 = 22
B saving = 45 − 18 = 27
C saving = 60 − 22 = 38
So savings ratio = 22 : 27 : 38 exactly.
Therefore:
x : y = 3 : 2
Common expenditure unit : common income unit = 2 : 3
✅ Final Answer
2 : 3
📌 Question 15 – Worker Efficiency
📝 Question
Three machines A, B, and C complete the same type of work.
Their efficiencies are in the ratio 5 : 6 : 8.
Machine A works for 18 days, Machine B for 15 days, and Machine C for 12 days.
During the last 6 days of operation, Machine B works at 80% of its normal efficiency, while Machine C works at 125% of its normal efficiency throughout its working period.
Find the ratio of the total work done by A, B, and C.
⚡ Shortcut Method
A:
5 × 18 = 90
B:
First 9 days = 6 × 9 = 54
Last 6 days = 6 × 80% × 6 = 28.8
Total = 82.8
C:
8 × 125% × 12 = 120
Therefore:
90 : 82.8 : 120
= 75 : 69 : 100
✅ Final Answer
75 : 69 : 100
📌 Question 16 – Production & Manufacturing
📝 Question
Three manufacturing units X, Y, and Z produce LED bulbs. Their daily production capacities are in the ratio 12 : 15 : 18.
During a 30-day production cycle:
- Unit X remained closed for 5 days.
- Unit Y remained closed for 3 days.
- Unit Z remained closed for 6 days.
- During its last 12 working days, Unit Y operated at 80% of its normal capacity.
- During the last 10 working days, Unit Z operated at 125% of its normal capacity.
Find the ratio of the total production of X : Y : Z during the month.
⚡ Shortcut Method
X works 25 days:
12 × 25 = 300
Y works 27 days.
First 15 working days:
15 × 15 = 225
Last 12 days at 80%:
15 × 80% × 12 = 144
Total Y = 369
Z works 24 days.
First 14 days:
18 × 14 = 252
Last 10 days at 125%:
18 × 125% × 10 = 225
Total Z = 477
Ratio:
300 : 369 : 477
= 100 : 123 : 159
✅ Final Answer
100 : 123 : 159
📌 Question 17 – Population Growth
📝 Question
The populations of three towns A, B, and C are in the ratio 8 : 10 : 15.
During the next year:
- Town A grows by 25%.
- Town B grows by 20%.
- Town C grows by 12%.
After growth, 3,400 people migrate from Town C to Town A.
If the final populations of A and C become equal, find the initial population of Town B.
⚡ Shortcut Method
Initial:
A = 8x
B = 10x
C = 15x
After growth:
A = 8x × 125% = 10x
B = 10x × 120% = 12x
C = 15x × 112% = 16.8x
After 3,400 migrate from C to A:
A = 10x + 3,400
C = 16.8x − 3,400
Given they become equal:
10x + 3,400 = 16.8x − 3,400
6.8x = 6,800
x = 1,000
Initial B = 10 × 1,000 = 10,000
✅ Final Answer
10,000
📌 Question 18 – Business Profit Sharing
📝 Question
Four partners A, B, C, and D invested in a startup in the ratio 6 : 8 : 10 : 12.
After 6 months:
- A doubled his investment.
- B withdrew 25%.
- C made no change.
- D increased his investment by 50%.
The annual profit earned was ₹20,50,000.
Find the difference between the profit shares of D and B.
⚡ Shortcut Method
Weighted investments:
A = 6 × 6 + 12 × 6 = 108
B = 8 × 6 + 6 × 6 = 84
C = 10 × 12 = 120
D = 12 × 6 + 18 × 6 = 180
Ratio:
108 : 84 : 120 : 180
= 9 : 7 : 10 : 15
D − B = 15 − 7 = 8 parts
Total parts = 41
One part:
₹20,50,000 ÷ 41 = ₹50,000
Difference:
8 × ₹50,000 = ₹4,00,000
✅ Final Answer
₹4,00,000
📌 Question 19 – Hidden Combined Ratio
📝 Question
The ratio of incomes of A : B = 5 : 7, and the ratio of incomes of B : C = 4 : 9.
The ratio of their expenditures is 16 : 24 : 59.
If all three save equal amounts and their combined monthly income is ₹22,20,000, find the monthly expenditure of C.
⚡ Shortcut Method
Income ratios:
A : B = 5 : 7
B : C = 4 : 9
Making B common:
A : B : C = 20 : 28 : 63
Total = 111 parts.
₹22,20,000 ÷ 111 = ₹20,000 per income unit.
Therefore:
A = ₹4,00,000
B = ₹5,60,000
C = ₹12,60,000
Expenditure ratio:
16 : 24 : 59
Because savings are equal:
A expenditure = ₹3,20,000 → saving ₹80,000
B expenditure = ₹4,80,000 → saving ₹80,000
C expenditure = ₹11,80,000 → saving ₹80,000
Therefore C’s expenditure = ₹11,80,000
✅ Final Answer
₹11,80,000
📌 Question 20 – 👑 BrainQuro Grand Challenge
📝 Question
A company has three factories P, Q, and R.
Initially, their monthly production capacities are in the ratio 9 : 12 : 15.
During the first half of the month:
- P operates at 100% capacity.
- Q operates at 90% capacity.
- R operates at 80% capacity.
During the second half:
- P operates at 120% capacity.
- Q returns to 100% capacity.
- R operates at 150% capacity.
Out of the total production:
- 5% of P’s output is defective.
- 8% of Q’s output is defective.
- 10% of R’s output is defective.
Find the ratio of the non-defective production of P : Q : R.
⚡ Shortcut Method
P:
9 × (15 × 100% + 15 × 120%)
= 9 × (15 + 18)
= 297
Non-defective P:
297 × 95% = 282.15
Q:
12 × (15 × 90% + 15)
= 12 × 28.5
= 342
Non-defective Q:
342 × 92% = 314.64
R:
15 × (15 × 80% + 15 × 150%)
= 15 × 34.5
= 517.5
Non-defective R:
517.5 × 90% = 465.75
Ratio:
282.15 : 314.64 : 465.75
Multiply by 100:
28,215 : 31,464 : 46,575
Divide by 9:
3,135 : 3,496 : 5,175
✅ Final Answer
3135 : 3496 : 5175
📚 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 3
💡 Shortcut Trick of the Day
When a partnership question involves changing investments, always calculate:
Investment × Time
for each investment period separately. Then add the weighted investments before simplifying the final ratio. This method is faster and avoids common mistakes in Banking Mains exams.
🎯 Challenge Question
Three investors A, B, and C invest in the ratio 7 : 9 : 12. After 4 months, A doubles his investment, B withdraws one-third of his investment, and C increases his investment by 50% after 8 months. If the annual profit is ₹18,48,000, determine the final profit-sharing ratio.
(Do not solve immediately—attempt it yourself first.)
⚠️ Common Mistakes
- Ignoring time while calculating partnership ratios.
- Simplifying ratios before accounting for all changes.
- Confusing efficiency ratio with time ratio.
- Mixing income ratios with savings ratios incorrectly.
- Forgetting that mixture replacement removes both components proportionally.
- Using approximate values too early in calculations.
