Bank Exams Percentage Questions with Detailed Solutions

Total income = 20000 Rs
Saving = x Rs
Saving % =x/20000×100=x/200%
New, salary = 35000
New saving =$$\frac{(35000×x)}{(200×100)}=\frac{7}{4}$$​x Rs
percentage increase in saving = $$\frac{\frac{7}{4} x-x}{x}\times100 = 75 \%$$

Exam Hall Method: 

​$$\textbf{Information Given:} \\33 \frac{1}{3}\% \text{ (i.e., } \frac{1}{3}) \text{ oranges were stolen} \\Remaining oranges = \frac{2}{3} \text{ of total} \\30\% \text{ of remaining were rotten} \Rightarrow 70\% \text{ were good} \\\text{Number of good oranges = 140} \\\textbf{Concept/Formula Used:} \\\text{Successive percentage concept} \\\text{Good} = \text{Total} \times \frac{2}{3} \times \frac{70}{100} \\\textbf{Explanation:} \\\text{Let total number of oranges = } x \\\text{Good oranges} = \frac{2}{3} \times \frac{70}{100} \times x \\= \frac{140}{300}x = \frac{7}{15}x \\\frac{7}{15}x = 140 \\x = 140 \times \frac{15}{7} \\x = 20 \times 15 = 300 \\\textbf{Final Answer: 300}$$​​

Given
Population ratio A : B = 5 : 6
Literate in A = 40%
Literate in B =$$66 \frac{2}{3}$$​%
Difference in illiterates = 600

Formula Used
Illiterate = Total − Literate

Solution
Let population of A = 5x and B = 6x
Illiterate in A = 60% of 5x = 3x
Illiterate in B = $$33 \frac{1}{3}$$​% of 6x = 2x
Difference = 3x − 2x = x = 600
Population of A = 5x = 3000

Final Answer
So the correct answer is (b)

​Exam Hall Method: ​

Given
Total population = 160000
Male increase = 8%
Female increase = 20%
Final ratio = 3 : 2

Formula Used
Population after increase = Original × (1 + Rate)

Solution
Let original male = M and female = F
M + F = 160000

After increase:
Male = 1.08M
Female = 1.20F
​$$\frac{1.08M}{1.20F} = \frac{3}{2}$$​​
​$$\frac{M}{F} = \frac{5}{3}$$​​
M = 100000 and F = 60000

Final Answer
So the correct answer is (b)

​Exam Hall Method: ​

Given
A income = 75% of B income
A expenditure = 60% of B expenditure
A income = 80% of B expenditure

Formula Used
Savings = Income − Expenditure

Solution
Let B expenditure = 100
Then A income = 80
B income = $$\frac{80}{0.75} = \frac{320}{3}$$​​
A expenditure = 60
A savings = 80 − 60 = 20
B savings = $$\frac{320}{3} − 100 = \frac{20}{3}$$​​
Ratio = 20 :$$\frac{20}{3}$$​ = 3 : 1

Final Answer
So the correct answer is (d)

​Exam Hall Method: ​

$$\textbf{Given:}\\40\% \text{ of } Y = 48\\X \text{ is } 300\% \text{ more than } Y\\Y \text{ is } 150\% \text{ more than } Z\\[6pt]\textbf{Concept Used:}\\\text{Percentage increase}\\[6pt]\textbf{Formula Used:}\\A = \left(1 + \frac{p}{100}\right)B\\[6pt]\textbf{Solution:}\\0.4Y = 48\\Y = \frac{48}{0.4} = 120\\Y = 2.5Z\\Z = \frac{120}{2.5} = 48\\X = 4Y = 4 \times 120 = 480\\X - Z = 480 - 48 = 432\\[6pt]\textbf{Final Answer:}\\\boxed{432}$$​​

Exam Hall Method:

​$$\text{Given:}\\\text{Average income} = 14500\\\text{Difference of income} = 2500\\\text{A saves } 20\%,\;\text{B saves } 30\%\\[6pt]\text{Concept Used:}\\\text{Average and expenditure calculation}\\[6pt]\text{Formula Used:}\\\text{Average} = \frac{\text{Sum}}{2}\\\text{Expenditure} = \text{Income} - \text{Savings}\\[6pt]\text{Solution:}\\\text{Total income} = 14500 \times 2 = 29000\\\text{Let B's income} = x\\\text{A's income} = x + 2500\\[6pt]x + (x+2500) = 29000\\2x + 2500 = 29000\\2x = 26500\\x = 13250\\[6pt]\text{Income of A} = 15750\\\text{Savings of A} = 20\% \times 15750 = 3150\\\text{Savings of B} = 30\% \times 13250 = 3975\\[6pt]\text{Expenditure of A} = 15750 - 3150 = 12600\\\text{Expenditure of B} = 13250 - 3975 = 9275\\[6pt]\text{Total expenditure} = 12600 + 9275 = 21875\\[6pt]\text{Final Answer:}\\\boxed{21875}$$

​​Exam Hall Approach

​$$\text{Given} \\\text{Salary of B} = x \\\text{Salary of A} = 20\% \text{ more than B} \\\text{Salary of C} = 40\% \text{ more than B} \\\text{Concept Used} \\\text{Percentage comparison} \\\text{Formula Used} \\\text{Increased value} = \left(1 + \frac{p}{100}\right)\times \text{Original value} \\\text{Required percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \\\text{Solution} \\A = 1.20x \\C = 1.40x \\\frac{C}{A} \times 100 = \frac{1.40x}{1.20x} \times 100 \\= \frac{14}{12} \times 100 \\= 116.67\% \approx 117\% \\\text{Final Answer} \\117\%$$​​

$$\text{Given} \\\text{Amount Vasuki had} = x \\\text{Amount given to Nithi} = 80\% \text{ of } x \\\text{Fraction given by Nithi to Saratha} = \frac{3}{5} \\\text{Taxi fare paid by Saratha} = 500 \\\text{Amount left with Saratha} = 5260 \\\text{Concept Used} \\\text{Percentage and fractional distribution} \\\text{Formula Used} \\\text{Percentage value} = \frac{p}{100} \times \text{Total} \\\text{Fractional value} = \frac{m}{n} \times \text{Total} \\\text{Solution} \\\text{Amount received by Saratha} = 5260 + 500 = 5760 \\\frac{3}{5} \times \text{Amount received by Nithi} = 5760 \\\text{Amount received by Nithi} = \frac{5760 \times 5}{3} = 9600 \\0.80x = 9600 \\x = \frac{9600}{0.80} = 12000 \\\text{Final Answer} \\12000$$​​

​$$\text{Given} \\\text{Total number of balls} = x \\\text{Red balls} = 45\% \text{ of } x \\\text{Remaining balls} = 55\% \text{ of } x \\\text{Blue balls} = 60\% \text{ of remaining balls} \\\text{Yellow balls} = 44 \\\text{Concept Used} \\\text{Percentage distribution} \\\text{Formula Used} \\\text{Percentage value} = \frac{p}{100} \times \text{Total} \\\text{Solution} \\\text{Red balls} = 0.45x \\\text{Remaining balls} = x - 0.45x = 0.55x \\\text{Blue balls} = 0.60 \times 0.55x = 0.33x \\\text{Yellow balls} = 0.55x - 0.33x = 0.22x \\0.22x = 44 \\x = \frac{44}{0.22} = 200 \\\text{Final Answer} \\200$$​​

Given:

Invalid votes = 20% 

candidate A gets 40% of the valid votes

A  lose by 80 votes.

Explanation:

$$\text{Let total vote be } 100x \\\text{Valid vote} = \frac{80}{100} \times 100x = 80x \\\text{ATQ,} \\\frac{60}{100} \times 80x - \frac{40}{100} \times 80x = 80 \\48x - 32x = 80 \\16x = 80 \\x = 5 \\\text{Total votes} = 500$$​

Given:
Percentage of voters who did not vote = 20%
Percentage of invalid votes = 10%
Winning candidate's valid vote share = 55%
Margin of victory = 36 votes

Formula Used:
Margin = (% difference) × Valid Votes

Solution:
Let total votes cast = x
Invalid votes = 10% of x = $$\frac{x}{10}$$​
Valid votes = 90% of x = $$\frac{9x}{10}$$​
Winning candidate votes = 55%
Losing candidate votes = 45%
Difference = 55% − 45% = 10% = $$\frac{1}{10}$$​
Margin = $$\frac{1}{10}$$​ of valid votes
36 = $$\frac{1}{10}$$​ × $$\frac{9x}{10}$$​
36 = $$\frac{9x}{100}$$​
x =$$\frac{36 \times 100}{9}$$​
x = $$\frac{3600}{9}$$​ = 400
Final Answer: 400

Short Trick: 

Exam Hall Method: 

Information Given:
There are only two candidates: A and B
A got 60% fewer votes than B
If B got 600 votes less, both would have tied (equal votes)
Formula Used:
Percentage difference between two quantities
Explanation:
Let the number of votes received by B be x.
Then, A got 60% less than B, so A got:
A = x - 60% of x = x - (60/100)x = (40/100)x = 0.4x
So,
A = 0.4x
B = x
Now, the question says:
If B had got 600 votes less, there would have been a tie, i.e., both would have equal votes.
That means:
(x - 600) = 0.4x
Now solve:
x - 600 = 0.4x
x - 0.4x = 600
0.6x = 600
x = 600 / 0.6
x = 1000
So, B got 1000 votes.
Then A got 0.4 × 1000 = 400 votes
Total votes polled = A's votes + B's votes
= 400 + 1000 = 1400 votes​

Given: 

​ Ratio of income of A and B are in the ratio of 21:20

Explanation:

Exam Hall Method: