Percentage - Aptitude MCQ Questions and Solutions with Explanations

Let the cost of a single ticket be Rs. $$x$$
The, cost of monthly return ticket :
$$\eqalign{ & = 125\% \,\,{\text{of}}\,\,{\text{Rs}}.x \cr & = {\text{Rs}}{\text{. }}\left( {\frac{{125}}{{100}}x} \right) \cr & = {\text{Rs}}{\text{. }}\frac{{5x}}{4} \cr} $$
Cost of monthly return ticket with extension :
$$\eqalign{ & = 105\% \,\,{\text{of}}\,\,{\text{Rs}}.\frac{{5x}}{4} \cr & = {\text{Rs}}{\text{. }}\left( {\frac{{105}}{{100}} \times \frac{{5x}}{4}} \right) \cr & = {\text{Rs}}{\text{. }}\frac{{21x}}{{16}} \cr} $$
$$\eqalign{ & \therefore \frac{{21x}}{{16}} = 84 \cr & \Rightarrow x = \left( {\frac{{84 \times 16}}{{21}}} \right) \cr & \Rightarrow x = 64 \cr} $$

Quantity of pulp in fresh grapes = Quantity of pulp in dry grapes
= (100 - 10)% of 250 kg
= 90% of 250 kg
= 225 kg
Let the total weight of fresh grapes be $$x$$ kg
Then,
⇒ (100 - 80)% of $$x$$ = 225
⇒ 20% of $$x$$ = 225
⇒ $$\frac{x}{5}$$ = 225
⇒ $$x$$ = 225 × 5
⇒ $$x$$ = 1125
Hence, total weight of fresh grapes = 1125 kg

Let the person's gross income be Rs. $$x$$
Then,
⇒ (100 - 3)% of $$x$$ = 237650
⇒ 97% of $$x$$ = 237650
⇒ $$\frac{97x}{100}$$ = 237650
⇒ $$x$$ = $$\left( {\frac{{237650 \times 100}}{{97}}} \right)$$
⇒ $$x$$ = 245000
∴ When income tax is raised to 7%, we have :
Net income :
= (100 - 7)% of Rs. 245000
= 93% of Rs. 245000
= Rs. $$\left( {\frac{{93}}{{100}} \times 245000} \right)$$
= Rs. 227850

Number of games already won
= 30% of 60
= 18
Let the required number of games be $$x$$
Then,
$$\eqalign{ & \Rightarrow \frac{{18 + x}}{{60 + x}} \times 100 = 50 \cr & \Rightarrow \frac{{18 + x}}{{60 + x}} = \frac{1}{2} \cr & \Rightarrow 36 + 2x = 60 + x \cr & \Rightarrow x = 24 \cr} $$

Let the third number be $$x$$
Then, first number :
= $$112\frac{1}{2}\% $$  of $$x$$
= $$\frac{9x}{8}$$
Second number :
= 125% of $$x$$
= $$\frac{5x}{4}$$
∴ Required percentage :
= $$\left( {\frac{{9x}}{8} \times \frac{{4}}{{5x}} \times 100} \right)$$   %
= 90%

Let the original price be Rs. $$x$$
New final price :
= 110% of (110% of Rs. 100)
= Rs. $$\left( {\frac{{110}}{{100}} \times \frac{{110}}{{100}} \times 100} \right)$$
= Rs. 121
∴ Total increase :
= (121 - 100)%
= 21%

Let the total number of respondents be $$x$$
Percentage of uncertain individuals :
= [100 - (20 + 60)]%
= 20%
∴ 60% of $$x$$ - 20% of $$x$$ = 720
⇒ 40% of $$x$$ = 720
⇒ $$\frac{{40x}}{{100}}$$ = 720
⇒ $$x$$ = $$\left( {\frac{{720 \times 100}}{{40}}} \right)$$
⇒ $$x$$ = 1800

Let the total number of applicants be $$x$$
Number of eligible candidates = 95 % of $$x$$
Eligible candidates of other categories
= 15% of (95 of $$x$$)
= $$\left( {\frac{{15}}{{100}} \times \frac{{95}}{{100}} \times x} \right)$$
= $$\frac{{57x}}{{400}}$$
∴ $$\frac{{57x}}{{400}}$$ = 4275
⇒ $$x$$ = $$\left( {\frac{{4275 \times 400}}{{57}}} \right)$$
⇒ $$x$$ = 30000

Let the original price of sugar be Rs. 10 per kg
Then, original expenditure = Rs. (10 × 10) = Rs. 100
New expenditure = 110% of Rs. 100 = Rs. 110
New price of sugar = 132% of Rs. 10 = Rs. 13.20
New consumption :
= $$\frac{110}{13.20}$$ kg
= $$\frac{25}{3}$$ kg
= $$8\frac{1}{3}$$ kg

Number of questions answered correctly :
= 40% of 125
= 50
For 60% grade, number of questions to be answered correctly :
= 60% of 250
= 150
Remaining number of question to be answered correctly :
= 150 - 50
= 100
∴ Required percentage :
= $$\left( {\frac{{100}}{{125}} \times 100} \right)\% $$
= 80%