📖 Introduction
Mastering percentages is about more than simply calculating increases and decreases. In competitive exams, percentage concepts are often combined with profit and loss, mixtures, population changes, income analysis, examination marks, price changes, and work efficiency to create questions that require both speed and careful interpretation.
BrainQuro Percentage Questions Part 6 brings you 10 carefully verified questions covering Questions 51–60, designed around practical and exam-oriented situations. Each problem includes a shortcut solution to help you recognize percentage relationships quickly and reduce unnecessary calculations.
This practice set is especially useful for aspirants preparing for IBPS PO, SBI PO, RBI Assistant, LIC AAO, SSC CGL, RRB, Insurance Exams, and other competitive examinations.
Try solving each question independently before checking the shortcut method. The goal is not just to get the correct answer, but to develop the ability to identify the fastest possible approach under exam pressure.
Table of Contents
Question 51
📖 Question
A shopkeeper marks his goods 100% above the cost price and gives successive discounts of 25% and 20% to a customer. The customer then receives a 10% cashback on the final price, which is borne by the shopkeeper. Find the shopkeeper’s overall profit percentage.
📌 Information
- Markup = 100%
- First discount = 25%
- Second discount = 20%
- Cashback = 10% of final price
- Cashback is borne by the shopkeeper
- Find overall profit percentage
⚡ Shortcut Solution
Take CP = ₹100.
Marked Price: 100×200%=₹200
After 25% discount: 200×75%=₹150
After 20% discount: 150×80%=₹120
After 10% cashback: 120×90%=₹108
Profit: 108−100=₹8
Therefore, profit percentage = 8%.
✅ Final Answer
8% profit
Question 52
📖 Question
A container contains 40 litres of a milk-water mixture in the ratio 5 : 3. If 20% of the mixture is removed and replaced with pure water, and the process is repeated once more, find the final quantity of milk and its percentage in the mixture.
📌 Information
- Total mixture = 40 litres
- Milk : Water = 5 : 3
- Initial milk = 25 litres
- 20% mixture is replaced each time
- Process is repeated twice
- Find final milk quantity and percentage
⚡ Shortcut Solution
Initially: Milk=40×85=25 L
After each replacement, 80% of the milk remains.
After two replacements: 25×(80%)2 =25×0.64=16 L
Final milk percentage: 4016×100=40%
✅ Final Answer
16 litres of milk; 40% milk
Question 53
📖 Question
The population of a town increases by 20% in the first year, decreases by 25% in the second year, and increases by 10% in the third year. If the population at the end of three years is 49,500, find the initial population.
📌 Information
- First-year increase = 20%
- Second-year decrease = 25%
- Third-year increase = 10%
- Final population = 49,500
- Find initial population
⚡ Shortcut Solution
Use successive percentage multipliers: 120%×75%×110% =1.20×0.75×1.10=0.99
Thus, final population is 99% of the initial population. 99% of initial population=49,500
Therefore, Initial population=0.9949,500=50,000
✅ Final Answer
50,000
Question 54
📖 Question
A’s income is 25% more than B’s income, while B’s income is 20% less than C’s income. If C’s income increases by 25%, by what percentage should A’s income increase so that A’s income becomes exactly double C’s new income?
📌 Information
- A = 125% of B
- B = 80% of C
- C’s income increases by 25%
- New A must equal twice new C
- Find the required percentage increase in A’s income
⚡ Shortcut Solution
Take C’s income = ₹100.
Then: B=80 A=80×125%=100
New C: 100×125%=125
Required A: 2×125=250
A must increase from 100 to 250.
Therefore: 100250−100×100=150%
✅ Final Answer
150% increase
Question 55
📖 Question
In a company, 50% of the employees are men and the remaining 50% are women. Among the men, 20% are graduates, while 60% of the women are graduates. If the total number of non-graduate employees is 600, find the total number of employees in the company.
📌 Information
- Men = 50%
- Women = 50%
- Graduate men = 20%
- Graduate women = 60%
- Non-graduate employees = 600
- Find total employees
⚡ Shortcut Solution
Non-graduate men: 50%×80%=40%
Non-graduate women: 50%×40%=20%
Total non-graduates: 40%+20%=60%
Therefore: 60% of total employees=600 Total employees=0.60600=1,000
✅ Final Answer
1,000 employees
📚 Recommended Reading
- Previous Percentage Practice Set
- Next Percentage Questions Practice Set (Coming soon)
- Profit and Loss Questions with Answers
- Ratio and Proportions
Question 56
📖 Question
A trader sells two items at the same selling price of ₹6,000 each. On the first item, he makes a 10% profit, while on the second item, he incurs a 10% loss. Find his overall profit or loss percentage on the whole transaction.
📌 Information
- Selling price of each item = ₹6,000
- Profit on first item = 10%
- Loss on second item = 10%
- Find overall profit/loss percentage
⚡ Shortcut Solution
When two articles are sold at the same selling price, with equal profit and loss percentages: Overall loss=100r2
Here, r=10
Therefore, Loss=100102=1%
✅ Final Answer
1% loss
Question 57
📖 Question
A number X is first increased by 15%, then the result is decreased by 20%, and finally increased by 25%. If the final value exceeds the original number X by 84, find the value of X.
📌 Information
- First change = 15% increase
- Second change = 20% decrease
- Third change = 25% increase
- Final value exceeds original by 84
- Find X
⚡ Shortcut Solution
Combined multiplier: 115%×80%×125% =1.15×0.80×1.25 =1.15
Thus, final value is 15% greater than the original.
Therefore: 15% of X=84 X=0.1584 560
✅ Final Answer
560
Question 58
📖 Question
In a competitive examination, the maximum marks are 1,000, and a candidate needs 45% marks to pass. Candidate A scores 20% more than the passing marks, while Candidate B scores 10% less than A. Did Candidate B pass or fail, and by how many marks?
📌 Information
- Maximum marks = 1,000
- Passing percentage = 45%
- A scores 20% above passing marks
- B scores 10% below A
- Find whether B passes or fails and the margin
⚡ Shortcut Solution
Passing marks: 1000×45%=450
A’s marks: 450×120%=540
B’s marks: 540×90%=486
Difference from passing marks: 486−450=36
Therefore, B scores 36 marks above the passing marks.
✅ Final Answer
Candidate B passes by 36 marks.
Question 59
📖 Question
The price of sugar is reduced by 20%, due to which a family is able to buy 5 kg more sugar for ₹800 than before. Find the original price of sugar per kilogram.
📌 Information
- Price reduction = 20%
- Amount spent = ₹800
- Additional quantity purchased = 5 kg
- Find original price per kg
⚡ Shortcut Solution
Let the original price be ₹P per kg.
Original quantity: P800
New price: 80%P=0.8P
New quantity: 0.8P800
Additional quantity: 0.8P800−P800=5
Since 0.8P800=P1000
we get: P1000−800=5 P200=5 P=40
✅ Final Answer
₹40 per kg
Question 60
📖 Question
A alone can complete 40% of a work in 8 days. B is 25% more efficient than A. If both work together, in how many days will they complete 150% of the original work?
📌 Information
- A completes 40% work in 8 days
- B is 25% more efficient than A
- A and B work together
- Required work = 150% of the original work
- Find the required time
⚡ Shortcut Solution
A’s rate: 840%=5% per day
B is 25% more efficient: 5%×125%=6.25% per day
Combined rate: 5%+6.25%=11.25% per day
For 150% work: 11.25150=340 =1331 days
✅ Final Answer
13⅓ days
🎯 Challenge Question
📖 Question
A company has 40% of its employees working in Production and the remaining employees working in Administration and Sales. The number of employees in Administration is 25% less than the number in Sales. During a restructuring process, 20% of Production employees and 30% of Administration employees are transferred to another branch, while 10% of Sales employees are newly recruited.
After these changes, the company has 4,680 employees across these three departments. What was the company’s original number of employees?
📌 Information
- Production = 40% of original employees
- Administration + Sales = 60%
- Administration is 25% less than Sales
- 20% of Production employees are transferred
- 30% of Administration employees are transferred
- Sales employees increase by 10%
- Final total employees = 4,680
- Find the original number of employees
💡 Challenge: Try solving this without using a conventional equation. Look for a percentage-parts relationship.
⭐ Shortcut Trick of the Day
Successive Percentage Changes: Think in Multipliers
When a value undergoes several percentage changes, don’t calculate each change separately. Convert every change into a multiplier.
| Change | Multiplier |
|---|---|
| +20% | × 1.20 |
| −20% | × 0.80 |
| +25% | × 1.25 |
| −25% | × 0.75 |
| +10% | × 1.10 |
| −10% | × 0.90 |
For example:
Increase by 20%, decrease by 25%, then increase by 10% 1.20×0.75×1.10=0.99
So the final value is 99% of the original, meaning there is an overall 1% decrease.
🧠 BrainQuro Speed Rule
Successive changes → Convert to multipliers → Multiply → Compare with 100%.
This is usually much faster and safer than repeatedly calculating the percentage change in long steps
