🚀Introduction
Welcome back, aspirants! Ready to level up your Quantitative Aptitude?
Welcome to Part 3 of our exclusive percentage mastery series for IBPS PO, SBI PO, RBI Assistant, and SSC CGL Mains! 🎯 Since percentages drive everything from Data Interpretation to Profit & Loss, mastering high-level concepts is key to crushing the exam.
Dive into these 10 brand-new, challenging questions (Q21–Q30) packed with lightning-fast shortcut methods to save precious seconds in the exam hall. ⚡
Grab your notebook, sharpen your pencils, and let’s conquer these advanced sets together! ✨
Table of Contents
Question 21
📝 Question
A company increased the price of a premium laptop by 20%. During a festive sale, it offered a 15% discount on the increased price. An additional 5% cashback was credited to the customer’s account after purchase. If the customer effectively spent ₹77,520, find the original price of the laptop.
📌 Information
- Price Increase = 20%
- Discount = 15%
- Cashback = 5%
- Effective Amount Paid = ₹77,520
⚡ Shortcut Solution
Assume the original price = 100 parts
After 20% increase:
100 → 120 parts
After 15% discount:
120 × 85% = 102 parts
After 5% cashback:
102 × 95% = 96.9 parts
So,
96.9 parts = ₹77,520
1 part = ₹800
Original price = 100 × ₹800
= ₹80,000
✅ Final Answer
₹80,000
Question 22
📝 Question
In an examination, 30% of the students failed in Mathematics, 25% failed in English, and 10% failed in both subjects. If 1,650 students passed in both subjects, find the total number of students who appeared in the examination.
📌 Information
- Failed in Mathematics = 30%
- Failed in English = 25%
- Failed in Both = 10%
- Passed in Both = 1,650
⚡ Shortcut Solution
Students passing both
= 100% − (30% + 25% − 10%)
= 55%
So,
55% = 1,650
1% = 30
100% = 3,000
✅ Final Answer
3,000 Students
Question 23
📝 Question
The production of a factory increased by 25% in the first year. In the second year, 10% of the total production was rejected due to quality issues, and the remaining production was 20% higher than the original production. Find the percentage increase in production during the second year (before rejection).
📌 Information
- First Year Increase = 25%
- Rejection = 10%
- Final Accepted Production = 20% above Original
⚡ Shortcut Solution
Assume original production = 100 parts
After first year:
100 → 125 parts
Let second-year production = x
After rejecting 10%,
Accepted production = 90% of x
Given accepted production = 120 parts
So,
90% of x = 120
x = 120 ÷ 0.9
= 133⅓ parts
Increase over first year
= 133⅓ − 125
= 8⅓ parts
Percentage increase
= (8⅓ ÷ 125) × 100
= 6⅔%
✅ Final Answer
6⅔% Increase
Question 24
📝 Question
A dealer purchased an electronic appliance and marked it 50% above the cost price. He allowed two successive discounts of 20% and 10%. After this, he paid a commission equal to 5% of the selling price to an online marketplace. If his net profit was ₹8,100, find the cost price of the appliance.
📌 Information
- Markup = 50%
- Discounts = 20%, 10%
- Commission = 5% of Selling Price
- Net Profit = ₹8,100
⚡ Shortcut Solution
Assume cost price = 100 parts
Marked price = 150 parts
After 20% discount:
150 → 120 parts
After 10% discount:
120 → 108 parts
Commission = 5% of 108
= 5.4 parts
Net receipt = 108 − 5.4 = 102.6 parts
Profit = 2.6 parts
Given,
2.6 parts = ₹8,100
1 part = ₹8,100 ÷ 2.6
= ₹3,115.38
Cost price
= 100 × ₹3,115.38
≈ ₹3,11,538.46
✅ Final Answer
₹3,11,538.46
Question 25
📝 Question
The population of a town increased by 20% in the first year. During the second year, 10% of the population migrated to another city, after which 6,480 new residents joined the town. If the final population became 1,36,080, find the original population.
📌 Information
- First Year Increase = 20%
- Migration = 10%
- New Residents = 6,480
- Final Population = 1,36,080
⚡ Shortcut Solution
Population before new residents
= 1,36,080 − 6,480
= 1,29,600
Assume original population = 100 parts
After 20% increase:
100 → 120 parts
After 10% migration:
120 → 108 parts
So,
108 parts = 1,29,600
1 part = 1,200
Original population
= 100 × 1,200
= 1,20,000
✅ Final Answer
1,20,000
Question 26
📝 Question
In an election, 20% of the registered voters did not cast their votes. Of the votes polled, 4% were declared invalid. The winning candidate secured 60% of the valid votes and defeated the other candidate by 2,304 votes. Find the total number of registered voters.
📌 Information
- Voters who did not vote = 20%
- Invalid votes = 4% of votes polled
- Winner secured = 60% of valid votes
- Victory Margin = 2,304 votes
⚡ Shortcut Solution
Assume total registered voters = 100 parts
Votes polled = 80 parts
Valid votes = 80 × 96% = 76.8 parts
Winner’s votes = 60% of 76.8 = 46.08 parts
Loser’s votes = 40% of 76.8 = 30.72 parts
Victory margin = 46.08 − 30.72 = 15.36 parts
15.36 parts = 2,304
1 part = 150
Total voters = 100 × 150
= 15,000
✅ Final Answer
15,000 voters
Question 27
📝 Question
The monthly salary of an employee was increased by 25%. Due to a revision in the tax policy, 12% of the revised salary was deducted as income tax. The employee then saved 40% of the remaining salary. If his monthly savings were ₹61,600, find his monthly salary before the increment.
📌 Information
- Salary Increase = 25%
- Income Tax = 12% of revised salary
- Savings = 40% of post-tax salary
- Monthly Savings = ₹61,600
⚡ Shortcut Solution
Assume original salary = 100 parts
After increment:
100 → 125 parts
After tax:
125 × 88% = 110 parts
Savings:
40% of 110 = 44 parts
44 parts = ₹61,600
1 part = ₹1,400
Original salary = 100 × ₹1,400
= ₹1,40,000
✅ Final Answer
₹1,40,000
Question 28
📝 Question
A factory manufactured a certain number of LED bulbs. During quality testing, 8% were rejected. Of the remaining bulbs, 25% were exported, while the rest were sold in the domestic market. If 27,600 bulbs were sold in the domestic market, find the total number of bulbs manufactured.
📌 Information
- Rejected = 8%
- Exported = 25% of accepted bulbs
- Domestic Sales = 27,600 bulbs
⚡ Shortcut Solution
Assume total production = 100 parts
After rejection:
100 → 92 parts
Domestic sales:
92 × 75% = 69 parts
69 parts = 27,600
1 part = 400
Total production = 100 × 400
= 40,000 bulbs
✅ Final Answer
40,000 bulbs
Question 29
📝 Question
The price of a commodity was first increased by 40% and then decreased by 25%. A customer purchased 240 units of the commodity for ₹2,52,000 after these changes. Find the original price per unit.
📌 Information
- Price Increase = 40%
- Price Decrease = 25%
- Quantity Purchased = 240 units
- Total Amount Paid = ₹2,52,000
⚡ Shortcut Solution
Final price per unit
= ₹2,52,000 ÷ 240
= ₹1,050
Assume original price = 100 parts
After 40% increase:
100 → 140 parts
After 25% decrease:
140 × 75% = 105 parts
105 parts = ₹1,050
1 part = ₹10
Original price = 100 × ₹10
= ₹1,000 per unit
✅ Final Answer
₹1,000 per unit
Question 30
📝 Question
In a company, 60% of the employees are males and the remaining are females. 35% of the male employees and 45% of the female employees work in the Sales department. If the total number of employees working in the Sales department is 780, find the total number of employees in the company.
📌 Information
- Male Employees = 60%
- Female Employees = 40%
- Male Employees in Sales = 35%
- Female Employees in Sales = 45%
- Total Sales Employees = 780
⚡ Shortcut Solution
Assume total employees = 100 parts
Male employees in Sales
= 60 × 35%
= 21 parts
Female employees in Sales
= 40 × 45%
= 18 parts
Total employees in Sales
= 21 + 18
= 39 parts
So,
39 parts = 780
1 part = 20
Total employees
= 100 × 20
= 2,000
✅ Final Answer
2,000 employees
⚡ Shortcut Trick of the Day: The Multiplier Chain Technique
For continuous multi-year percentage changes, always convert the percentages into simplified fractions first. Multiplying the base value by net fractional multipliers saves critical seconds during high-stakes Mains examinations compared to conventional decimal scaling.
📚 Recommended Reading
- Percentage Questions with Answers – Part 1
- Percentage Questions with Answers – Part 2
- Percentage Questions with Answers – Part 4
- Profit and Loss Questions with Answers
💬 Challenge Question for the Comments
Try solving this and drop your answers below:
A shopkeeper marks up his goods by 40% and offers a successive discount of 10% and 5% respectively. If he still makes a profit of Rs. 432, what was the cost price of the article?
Let us know your step-by-step approach in the comments section!
