Percentage - Aptitude MCQ Questions and Solutions with Explanations

Let 45% of 300 + $$\sqrt {x} $$ = 56% of 750 - 10% of 250
Then,
$$\left( {\frac{{45}}{{100}} \times 300} \right) + \sqrt x = \left( {\frac{{56}}{{100}} \times 750} \right)$$       $$ - \left( {\frac{{10}}{{100}} \times 250} \right)$$
$$\eqalign{ & \Rightarrow 135 + \sqrt x = 420 - 25 \cr & \Rightarrow \sqrt x = 260 \cr & \Rightarrow x = {\left( {260} \right)^2} \cr & \Rightarrow x = 67600 \cr} $$

Percentage increase :
$$\eqalign{ & = \left( {\frac{{21}}{{560}} \times 100} \right)\% \cr & = \frac{{15}}{4}\% \cr & = 3.75\% \cr} $$

Let the number be x
Then,
$$\eqalign{ & \Rightarrow \frac{{x + 75\% {\text{ of }}x + 25\% {\text{ of }}x}}{3} = 240 \cr & \Rightarrow x + \frac{{75}}{{100}}x + \frac{{25}}{{100}}x = 240 \times 3 \cr & \Rightarrow x + \frac{3}{4}x + \frac{1}{4}x = 720 \cr & \Rightarrow 2x = 720 \cr & \Rightarrow x = 360 \cr} $$

Number of runs made by running
= 110 - (3 × 4 + 8 × 6)
= 50
∴ Required percentage :
$$\eqalign{ & = \left( {\frac{{50}}{{110}} \times 100} \right)\% \cr & = 45\frac{5}{{11}}\% \cr} $$

Required percentage
$$\eqalign{ & = \left( {\frac{{0.01}}{{0.1}} \times 100} \right)\% \cr & = \left( {\frac{1}{{10}} \times 100} \right)\% \cr & = 10\% \cr} $$

Let the total number of votes be x
Then, votes polled = 90% of x
Valid votes = 90% of (90% of x)
∴ 54% of [90% of (90% of x)] - 46% of [90% of (90% of x)] = 1620
⇔ 8% of [90% of ((90% of x)] = 1620
⇔ $$\frac{8}{100}$$ × $$\frac{90}{100}$$ × $$\frac{90}{100}$$ × x = 1620
⇔ x = $$\left( {\frac{{1620 \times 100 \times 100 \times 100}}{{8 \times 90 \times 90}}} \right)$$
⇔ x = 25000

Let x - 6% of x = xz
Then,
⇔ 94% of x = xz
⇔ $$\frac{94x}{100}$$ × $$\frac{1}{x}$$ = z
⇔ z = 0.94

Let the total number of children be x
Then,
⇔ x × (20% of x) = 605
⇔ $$\frac{1}{5}$$x² = 605
⇔ x² = 3025
⇔ x = 55
∴ Number of sweets received by cash child
= 20% of 55 = 11

Asha's monthly income :
= 60% of 78000
$$\eqalign{ & = {\text{Rs}}{\text{. }}\left( {\frac{{60}}{{100}} \times 78000} \right) \cr & {\text{ = Rs}}{\text{. 46800}} \cr} $$
Let Maya's monthly income be Rs. x
Then,
120% of x = 46800
$$\eqalign{ & \Rightarrow {\text{x}} = \left( {\frac{{46800 \times 100}}{{120}}} \right) \cr & \Rightarrow {\text{x}} = 39000 \cr} $$

Let the distance be x km and the original time time taken be y hours.
Then,
Original speed = $$\frac{x}{y}$$ km/hr
New speed :
$$\eqalign{ & = \left( {\frac{x}{{80\% {\text{ of }}y}}} \right){\text{ km/hr}} \cr & = \left( {\frac{5}{4}.\frac{x}{y}} \right){\text{ km/hr}} \cr} $$
Increase in speed :
$$\eqalign{ & {\text{ = }}\left( {\frac{{5x}}{{4y}} - \frac{x}{y}} \right) \cr & {\text{ = }}\frac{x}{{4y}} \cr} $$
∴ Increase %
$$\eqalign{ & {\text{ = }}\left( {\frac{x}{{4y}} \times \frac{y}{x} \times 100} \right)\% \cr & = 25\% \cr} $$