Percentage - Aptitude MCQ Questions and Solutions with Explanations

Answer: Option D

$$\eqalign{ & n\left( A \right) = \left( {\frac{{75}}{{100}} \times 600} \right) = 450 \cr & n\left( B \right) = \left( {\frac{{45}}{{100}} \times 600} \right) = 270 \cr & \therefore n\left( {A \cap B} \right) \cr} $$
$$ = n\left( A \right) + n\left( B \right) - n\left( {A \cup B} \right)$$     $$n\left( {A \cup B} \right)$$   $$ -\, 600$$
$$\eqalign{ & = \left( {450 + 270 - 600} \right) \cr & = 120 \cr} $$

Answer: Option B

Let original income = Rs. 100
Then, saving = Rs. 20 and expenditure = Rs. 80
New income :
$$=$$ Rs. $$116\frac{2}{3}$$
$$=$$ Rs. $$\frac{350}{3}$$
New expenditure :
$$=$$ $$137\frac{1}{2}$$ % of Rs. 80
$$=$$ Rs. $$\left( {\frac{{275}}{2} \times \frac{1}{{100}} \times 80} \right)$$
$$=$$ Rs. 110
New saving :
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {\frac{{350}}{3} - 110} \right) \cr & = {\text{Rs}}{\text{.}}\frac{{20}}{3} \cr} $$
∴ Required percentage
$$\eqalign{ & = \left( {\frac{{20}}{3} \times \frac{3}{{350}} \times 100} \right)\% \cr & = \frac{{40}}{7}\% \cr & = 5\frac{5}{7}\% \cr} $$

Answer: Option A

Let the total number of candidates be x
Number of capable candidates who got admitted to college :
= 80% of 40% of x
$$\eqalign{ & = \left( {\frac{{80}}{{100}} \times \frac{{40}}{{100}} \times x} \right) \cr & = \frac{{8x}}{{25}} \cr} $$
Number of incapable college students :
= 25% of (100 - 40)% of x
$$\eqalign{ & = \left( {\frac{{25}}{{100}} \times \frac{{60}}{{100}} \times x} \right) \cr & = \frac{{3x}}{{20}} \cr} $$
Total number of candidates who got admitted to college :
$$=$$ $$\frac{{8x}}{{25}}$$ + $$\frac{{3x}}{{20}}$$
$$=$$ $$\frac{{47x}}{{100}}$$
∴ Required percentage :
$$\eqalign{ & = \left( {\frac{{8x}}{{25}} \times \frac{{100}}{{47x}} \times 100} \right)\% \cr & = \left( {\frac{{3200}}{{47}}} \right)\% \cr & = 68.09\% \approx 68\% \cr} $$