📖 Introduction
Percentage is not just a standalone chapter in Quantitative Aptitude—it is the base of many important arithmetic topics. A strong understanding of percentages makes it easier to handle Profit and Loss, Ratio and Proportion, Simple and Compound Interest, Mixtures, Data Interpretation, and several other questions commonly asked in competitive examinations.
In BrainQuro Percentage Questions with Answers– Part 7, Questions 61–70 are designed around different situations rather than repeating the same percentage formula. You will encounter problems involving successive percentage changes, mixture replacement, population growth, income comparison, employee analysis, profit and loss, examination marks, price reduction, and business revenue.
The real challenge in these questions is often not the calculation itself. It is identifying which quantity should be treated as the base and understanding how one percentage change affects the next. That is why each question is followed by a concise shortcut solution designed to develop faster problem-solving habits.
If you are strengthening your overall Quantitative Aptitude preparation, you can also explore related BrainQuro topics such as Profit and Loss Questions, Ratio and Proportion Questions, Simple and Compound Interest Questions, Mixture and Alligation Questions, and Data Interpretation Questions.
Tip: Try to solve each question before looking at the shortcut solution. Your goal should be to find the shortest accurate method, not merely the final answer.
Whether you are preparing for SBI PO, IBPS PO, RBI Assistant, LIC AAO, SSC CGL, RRB, Insurance Exams, or other competitive examinations, this set is designed to help you build the percentage skills needed for tougher arithmetic questions.
Start with Question 61, keep your calculations precise, and see how quickly you can complete all 10 questions.
Table of Contents
Question 61
📖 Question
A shopkeeper marks his goods 40% above the cost price and gives successive discounts of 10% and 15% to a customer. If the customer further gets a 5% cashback on the final discounted price, which is borne by the shopkeeper, find the shopkeeper’s overall profit percentage.
📌 Information
- Markup = 40%
- First discount = 10%
- Second discount = 15%
- Cashback = 5%
- Cashback is borne by the shopkeeper
- Find overall profit percentage
⚡ Shortcut Solution
Take the cost price as ₹100.
Marked price:
₹100 × 140% = ₹140
After 10% discount:
₹140 × 90% = ₹126
After 15% discount:
₹126 × 85% = ₹107.10
Cashback paid by the shopkeeper:
₹107.10 × 5% = ₹5.355
Effective amount received:
₹107.10 − ₹5.355 = ₹101.745
Profit:
₹101.745 − ₹100 = ₹1.745
✅ Final Answer
1.745% profit
Question 62
📖 Question
A container has a mixture of milk and water 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 percentage of milk in the container.
📌 Information
- Milk : Water = 5 : 3
- Initial milk = 5/8 of the mixture
- 20% of the mixture is removed each time
- Pure water replaces the removed mixture
- Process is repeated twice
- Find final milk percentage
⚡ Shortcut Solution
Initial milk percentage:
5 ÷ 8 × 100 = 62.5%
After each replacement, 80% of the milk remains.
After two replacements:
62.5% × 80% × 80%
= 40%
✅ Final Answer
40% milk
Question 63
📖 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 percentage multipliers:
120% × 75% × 110%
= 1.20 × 0.75 × 1.10
= 0.99
Therefore, the final population is 99% of the initial population.
So:
99% of initial population = 49,500
Initial population:
49,500 ÷ 99% = 50,000
✅ Final Answer
50,000
Question 64
📖 Question
A’s income is 25% more than B’s income, and 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’s income = 125% of B’s income
- B’s income = 80% of C’s income
- C’s income increases by 25%
- New A’s income must be twice the new C’s income
- Find the percentage increase required in A’s income
⚡ Shortcut Solution
Take C’s income as ₹100.
B’s income:
₹100 × 80% = ₹80
A’s income:
₹80 × 125% = ₹100
C’s new income:
₹100 × 125% = ₹125
Required A’s income:
₹125 × 2 = ₹250
A must increase from ₹100 to ₹250.
Increase:
₹250 − ₹100 = ₹150
Percentage increase:
₹150 ÷ ₹100 × 100 = 150%
✅ Final Answer
150% increase
Question 65
📖 Question
In a company, 50% of 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:
600 ÷ 60% = 1,000
✅ Final Answer
1,000 employees
📚 Recommended Reading
- Percentage Questions With Answers Practice Set Part 6
- Percentage Questions With Answers Practice Set Part 8 (Coming Soon)
- Profit and Loss Questions with Answers
- Ratio and Proportions
Question 66
📖 Question
A trader sells two items at the same selling price of ₹5,940 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 = ₹5,940
- Profit on first item = 10%
- Loss on second item = 10%
- Both selling prices are equal
- 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 = 10² ÷ 100
= 1%
✅ Final Answer
1% loss
Question 67
📖 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 value by 84
- Find X
⚡ Shortcut Solution
Combined multiplier:
115% × 80% × 125%
= 1.15 × 0.80 × 1.25
= 1.15
Therefore, the final value is 15% more than X.
So:
15% of X = 84
X = 84 ÷ 15%
= 560
✅ Final Answer
560
Question 68
📖 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% more than passing marks
- B scores 10% less than A
- Find whether B passes or fails
- Find the margin
⚡ Shortcut Solution
Passing marks:
1,000 × 45% = 450
A’s marks:
450 × 120% = 540
B’s marks:
540 × 90% = 486
Difference:
486 − 450 = 36
✅ Final Answer
Candidate B passes by 36 marks.
Question 69
📖 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:
₹800 ÷ P
New price:
P × 80% = 0.8P
New quantity:
₹800 ÷ 0.8P
The additional quantity is 5 kg.
Therefore:
800 ÷ 0.8P − 800 ÷ P = 5
Since:
800 ÷ 0.8P = 1,000 ÷ P
Therefore:
1,000 ÷ P − 800 ÷ P = 5
200 ÷ P = 5
P = ₹40
✅ Final Answer
₹40 per kg
Question 70
📖 Question
A company’s revenue increases by 25% in the first quarter and decreases by 20% in the second quarter. In the third quarter, the revenue increases by 15%. If the revenue at the end of the third quarter is ₹27.6 lakh, find the revenue at the beginning of the year.
📌 Information
- First-quarter increase = 25%
- Second-quarter decrease = 20%
- Third-quarter increase = 15%
- Final revenue = ₹27.6 lakh
- Find initial revenue
⚡ Shortcut Solution
Combined multiplier:
125% × 80% × 115%
= 1.25 × 0.80 × 1.15
= 1.15
Therefore, final revenue is 115% of the original revenue.
So:
115% of original revenue = ₹27.6 lakh
Original revenue:
₹27.6 lakh ÷ 115%
= ₹24 lakh
✅ Final Answer
₹24 lakh
🔥 BrainQuro Power Challenge
📖 Challenge Question
A company’s annual revenue increases by 20% in the first year and decreases by 10% in the second year. In the third year, its revenue increases by 25%. At the end of the third year, the revenue is ₹6.75 crore higher than the original revenue.
If the company’s profit margin was 16% of revenue initially, but increased to 20% of revenue at the end of the third year, find the increase in the company’s annual profit over the three-year period.
📌 Your Challenge
Do not calculate the three years separately.
Try to:
- Find the final revenue as a percentage of the original revenue.
- Determine the original revenue.
- Calculate the original and final profit.
- Find the increase in profit.
⏱️ Target Time: 60 seconds
⭐ Trick of the Day
The “Base-100” Rule
Whenever a percentage question contains multiple percentage changes, temporarily assume the original value is 100.
For example:
Increase by 20%, decrease by 10%, then increase by 25%.
Instead of carrying an unknown value:
100 → 120 → 108 → 135
So the final value is 135% of the original.
That immediately tells you:
Overall increase = 35%
🧠 BrainQuro Speed Rule
When the original value is unknown, make it 100 first.
This is particularly powerful in:
- Successive percentage changes
- Profit and loss
- Markup and discount
- Salary changes
- Population changes
- Price changes
- Revenue and expenditure problems
⚡ 30-Second Percentage Test
A product’s price is increased by 25% and then reduced by 20%. By what percentage is the final price different from the original price?
Don’t calculate using a long method.
Answer
No change — 0%
Because:
100 → 125 → 100
