Welcome to BrainQuro Percentage Practice Set 9, featuring 10 advanced percentage questions from Q81 to Q90.
Percentage Practice set 9 focuses on multi-concept problems involving elections, income and savings, examination results, taxation, price and consumption, mixtures, population growth, ratios, marks, and successive percentage changes.
These questions are designed for aspirants preparing for SBI PO, IBPS PO, RBI Assistant, LIC AAO, SSC CGL, RRB, Insurance Exams, and other competitive examinations.
Try each question yourself before checking the shortcut method. The goal is not only to get the correct answer but also to develop faster calculation techniques for competitive exams.
Table of Contents
Percentage Practice Set 9: Advanced Questions
Before moving to the Questions, make sure you have attempted all 10 questions from Percentage Practice Set 8 without looking at the shortcuts.
Question 81
📖 Question
In an election, 20% of registered voters did not cast their votes. 10% of the votes cast were declared invalid. The winning candidate secured 55% of the valid votes and won the election by 1,440 votes. Find the total number of registered voters in the voter list.
Options:
A) 15,000
B) 18,000
C) 20,000
D) 25,000
⚡ Shortcut Solution
Let total registered voters = 100%.
20% did not vote.
Votes cast = 80%
10% of votes cast were invalid.
Valid votes = 90% of 80%
= 72%
Winner secured 55% of valid votes.
Loser secured 45%.
Winning margin = 55% − 45%
= 10% of valid votes
Therefore:
10% of 72% = 7.2% of total voters
7.2% = 1,440
Total voters:
= 1,440 × 100 ÷ 7.2
= 20,000
✅ Final Answer
C) 20,000
Question 82
📖 Question
The incomes of A, B, and C are in the ratio 3 : 4 : 5, and their expenditures are in the ratio 2 : 3 : 4. If A saves 33.33% of his income, what is the combined percentage of savings of all three individuals taken together?
Options:
A) 20%
B) 22.5%
C) 25%
D) 30%
⚡ Shortcut Solution
Income ratio:
A : B : C = 3 : 4 : 5
A saves 33.33%, which is approximately 1/3 of income.
Therefore, A’s expenditure = 2/3 of income.
If A’s income = 3x:
A’s expenditure = 2x
Given expenditure ratio:
A : B : C = 2 : 3 : 4
Therefore:
B’s expenditure = 3x
C’s expenditure = 4x
Their incomes are:
A = 3x
B = 4x
C = 5x
Savings:
A = 3x − 2x = x
B = 4x − 3x = x
C = 5x − 4x = x
Total savings = 3x
Total income = 3x + 4x + 5x = 12x
Combined saving percentage:
= 3x ÷ 12x × 100
= 25%
✅ Final Answer
C) 25%
Question 83
📖 Question
In an entrance test, 60% of candidates passed in Quantitative Aptitude, 50% passed in Reasoning, and 40% passed in English. 20% passed in both QA and Reasoning, 15% passed in Reasoning and English, and 25% passed in QA and English. If 5% passed in all three subjects, and 45 candidates failed in all three subjects, find the total number of candidates who appeared for the test.
Options:
A) 750
B) 800
C) 900
D) 1000
⚡ Shortcut Solution
Candidates passing in at least one subject:
60% + 50% + 40% − 20% − 15% − 25% + 5%
= 95%
Therefore, candidates failing in all three:
100% − 95%
= 5%
Given:
5% = 45 candidates
Therefore:
100% = 45 × 100 ÷ 5
= 900
✅ Final Answer
C) 900
Advanced Percentage Questions For IBPS PO
Tough Ratio and Proportion Questions For Banking Exams
Question 84
📖 Question
The price of petrol increases by 25%. Due to a government policy, an additional 10% tax is levied on the new price. If a family wants to keep their total expenditure on petrol (including tax) higher by only 32% compared to the original base expenditure, by what percentage must they reduce their consumption of petrol?
Options:
A) 2.5%
B) 4%
C) 5%
D) 6.25%
⚡ Shortcut Solution
Original price = 100
After 25% increase:
= 125
Additional 10% tax on the new price:
= 125 × 110%
= 137.5
The desired expenditure is 32% higher than the original:
= 132
Therefore, required consumption factor:
= 132 ÷ 137.5
= 0.96
So consumption should become 96% of the original.
Required reduction:
100% − 96%
= 4%
✅ Final Answer
B) 4%
Question 85
📖 Question
Due to a 20% reduction in the price of sugar, a buyer can purchase 10 kg more sugar for Rs. 600. If the reduced price is subsequently increased by 50%, find the final price of sugar per kg.
Options:
A) Rs. 15
B) Rs. 16
C) Rs. 18
D) Rs. 20
⚡ Shortcut Solution
Let original price = P.
After a 20% reduction:
New price = 80% of P
Since the same ₹600 buys 10 kg more:
600 ÷ 0.8P − 600 ÷ P = 10
Solving:
600(1/0.8 − 1) ÷ P = 10
600 × 0.25 ÷ P = 10
150 ÷ P = 10
P = ₹15
Reduced price:
₹15 × 80%
= ₹12
Now the reduced price increases by 50%:
₹12 × 150%
= ₹18
✅ Final Answer
C) Rs. 18
Question 86
📖 Question
A vessel contains 250 litres of a mixture of milk and water where milk is 80% of the mixture. 50 litres of the mixture is drawn out and replaced with pure water. This process is repeated one more time. Find the final quantity of milk (in litres) left in the mixture.
Options:
A) 115 litres
B) 120 litres
C) 128 litres
D) 135 litres
⚡ Shortcut Solution
Initial milk:
80% of 250
= 200 litres
Each time 50 litres is removed from 250 litres.
Fraction of milk remaining each time:
200 ÷ 250 = 4/5
After first replacement:
200 × 4/5 = 160 litres
After second replacement:
160 × 4/5 = 128 litres
✅ Final Answer
C) 128 litres
Question 87
📖 Question
The population of a city increases successively over three years by 10%, 20%, and 25% respectively. If the difference between the final population after 3 years and the initial population is 32,760, find the initial population.
Options:
A) 45,000
B) 48,000
C) 50,400
D) 55,000
⚡ Shortcut Solution
Successive growth factor:
110% × 120% × 125%
= 1.10 × 1.20 × 1.25
= 1.65
Therefore final population = 165% of initial population.
Increase = 65%.
Given:
65% = 32,760
Initial population:
= 32,760 × 100 ÷ 65
= 50,400
✅ Final Answer
C) 50,400
Question 88
📖 Question
Three numbers A, B, and C are such that A is 40% less than B, and C is 50% more than the sum of A and B. If the difference between C and B is 350, find the value of A.
Options:
A) 120
B) 150
C) 180
D) 200
⚡ Shortcut Solution
A is 40% less than B.
Therefore:
A = 60% of B
A = 0.6B
So:
A + B = 1.6B
C is 50% more than A + B:
C = 1.5 × 1.6B
= 2.4B
Given:
C − B = 350
2.4B − B = 350
1.4B = 350
B = 250
A = 60% of 250
= 150
✅ Final Answer
B) 150
Question 89
📖 Question
In an examination, a candidate who scores 25% marks fails by 30 marks. Another candidate who scores 55% marks gets 30 marks more than the minimum passing marks. A third candidate scores 45% marks. Find the number of marks by which the third candidate’s score exceeds the passing marks.
Options:
A) 5 marks
B) 10 marks
C) 15 marks
D) 20 marks
⚡ Shortcut Solution
Difference between the first two candidates’ scores:
30 + 30 = 60 marks
Difference in their percentages:
55% − 25%
= 30%
Therefore:
30% of maximum marks = 60
Maximum marks:
= 60 × 100 ÷ 30
= 200
Passing marks:
25% of 200 + 30
= 50 + 30
= 80
Third candidate’s marks:
45% of 200
= 90
Excess over passing marks:
90 − 80
= 10 marks
✅ Final Answer
B) 10 marks
Question 90
📖 Question
The price of an article undergoes three successive operations: first an increase of 20%, followed by a discount of 15%, and finally another percentage increase of x%. If the net overall increase in the price from the original cost to the final price is 53%, find the value of x.
Options:
A) 40%
B) 45%
C) 50%
D) 60%
⚡ Shortcut Solution
Overall increase = 53%.
Therefore final value = 153% of original.
First increase:
× 1.20
Then 15% discount:
× 0.85
Combined effect:
1.20 × 0.85
= 1.02
Therefore:
1.02 × (1 + x/100) = 1.53
So:
1 + x/100 = 1.53 ÷ 1.02
= 1.50
Therefore:
x = 50%
✅ Final Answer
C) 50%
⚡ 30-Second Percentage Test
A product’s price increases by 20% and its consumption decreases by 20%.
What happens to the total expenditure?
Try solving it mentally before checking the answer.
Answer: 4% decrease
Because:
1.20 × 0.80 = 0.96
So the final expenditure is 96% of the original.
🔥 BrainQuro Power Challenge
A company’s revenue increases by 25% in the first year, decreases by 20% in the second year, and increases by 30% in the third year.
At the end of the third year, its revenue is ₹9.6 crore higher than the original revenue.
If its original profit margin was 15% and the final profit margin became 18%, find the increase in its annual profit.
Try this challenge without using a calculator.
⚠️ Common Mistakes to Avoid
1. Adding successive percentages
A 20% increase followed by a 15% decrease is not simply a 5% increase.
2. Forgetting the base
A percentage change must always be calculated from the correct original or current value.
3. Confusing votes cast with valid votes
In election questions, keep separate:
Registered voters → Votes cast → Invalid votes → Valid votes
4. Ignoring repeated replacement
In mixture questions, the removal-and-replacement operation must be applied again when the process is repeated.
5. Treating tax as a percentage of the original price
In Q84, the 10% tax is imposed on the new price after the 25% increase, not on the original price.
🎯 Conclusion
This Percentage Practice Set 9 (Q81–90) brings together several important percentage concepts, including election calculations, income and savings, inclusion-exclusion, taxation, price and consumption, mixtures, compound population growth, ratios, examination marks and successive percentage changes.
For competitive exams, speed matters as much as accuracy. Try solving these questions without looking at the solutions first, then compare your approach with the shortcuts provided above.
Keep practicing more advanced quantitative aptitude questions with BrainQuro and gradually build the calculation speed required for competitive examinations.
Before moving to the next set, make sure you have attempted all 10 questions from Percentage Practice Set 9 without looking at the shortcuts.
