Percentage - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & \frac{{250 \times \left( {x + 20} \right)}}{{100}} = \frac{{220 \times x}}{{100}} \times \frac{{125}}{{100}} \cr & 25x + 500 = 22 \times x \times \frac{5}{4} \cr & 100x + 2000 = 110x \cr & 10x = 2000 \cr & x = 200 \cr & \frac{{\left( {x + 50} \right) \times 10}}{{100}} = \frac{{250 \times 10}}{{100}} = 25 \cr & \frac{{x \times 15}}{{100}} = \frac{{200 \times 15}}{{100}} = 30 \cr & {\text{Less}}\% = \frac{5}{{30}} \times 100 = 16\frac{2}{3}\% \cr} $$

\[\begin{array}{*{20}{c}} {{\text{Income}}}&{{\text{Expenditure}}}&{{\text{Saving}}} \\ \begin{gathered} 600 \hfill \\ \,\,\,\,\,\,\,\,\,\,{ \downarrow ^{ + 10\% }} \hfill \\ 660 \hfill \\ \end{gathered} &\begin{gathered} 500 \hfill \\ \,\,\,\,\,\,\,\,\,{ \downarrow ^{ + 20\% }} \hfill \\ 600 \hfill \\ \end{gathered} &\begin{gathered} 100 \hfill \\ \hfill \\ 60 \hfill \\ \end{gathered} \end{array}\]
Decrease in saving = $$\frac{{40}}{{100}}$$ × 100 = 40%

$$\eqalign{ & {\bf{Given:}} \cr & {\text{A is }}80\% {\text{ more than B}} \cr & {\text{C is }}48\frac{4}{7}\% {\text{ less than A}} + {\text{B}} \cr & {\bf{Formula}}\,{\bf{used:}} \cr & 80\% \to \frac{4}{5} \cr & {\bf{Calculation:}} \cr & \Rightarrow {\text{A}} = \left( {1 + \frac{4}{5}} \right){\text{B}} = \frac{{9{\text{B}}}}{5} \cr & \Rightarrow {\text{C}} = \left( {100\% - 48\frac{4}{7}\% } \right)\left( {{\text{A}} + {\text{B}}} \right) \cr & \Rightarrow {\text{C}} = 51\frac{3}{7}\% \times \left( {\frac{{9B}}{5} + {\text{B}}} \right) \cr & \Rightarrow {\text{C}} = \frac{{3.6}}{7} \times \frac{{14{\text{B}}}}{5} \cr & \Rightarrow {\text{C}} = \frac{{7.2{\text{B}}}}{5} \cr & {\text{Difference between A and C}} = \frac{{1.8{\text{B}}}}{5} \cr & \Rightarrow {\text{Percentage}} = \frac{{\frac{{1.8{\text{B}}}}{5}}}{{\frac{{9{\text{B}}}}{5}}} \times 100 \cr & = 0.2 \times 100 \cr & = 20\% \cr & \therefore {\text{The required percentage}} = 20\% \cr & \cr & {\bf{Alternate}}\,{\bf{solution:}} \cr & {\text{Let the value of B be 100}} \cr & \Rightarrow {\text{A}} = 100 \times 180\% = 180 \cr & \Rightarrow \left( {{\text{A}} + {\text{B}}} \right) = 280 \cr & {\text{According to the question}} \cr & {\text{C}} = 51\frac{3}{7}\% {\text{ of }}280 \cr & \Rightarrow {\text{C}} = \frac{{360}}{{700}} \times 280 = 144 \cr & {\text{So, required }}\% = \frac{{180 - 144}}{{180}} \times 100\% = 20\% \cr & \therefore {\text{The required }}\% {\text{ is }}20\% \cr} $$

Rohit income = 32000
Cost = 30%
Saving = 70%
Saving = 32000 × $$\frac{{70}}{{100}}$$ = 22400

Before hike price → Rs. 82 per litre
5% → $$\frac{{82 \times 5}}{{100}}$$  = Rs. 4.1 per litre
Distance = 3045 km
Petrol use = $$\frac{{3045}}{{15}}$$  = 203
Increase expenditure = 203 × 4.1 = 832.3 = Rs. 832

$${l_1} \to {l_2}$$
\[10\xrightarrow[{ + 10 \uparrow }]{}{l_2}\]
$$\eqalign{ & {S_1} \to {S_2} \cr & 6 \times {10^2} \to 6 \times {11^2} \cr & 100 \to 121 \cr & = \frac{{21}}{{100}} \times 100 \cr & = 21\% \cr} $$

$$\eqalign{ & {\text{Let fraction}} = \frac{x}{y} \cr & \frac{{x\left( {115} \right)}}{{y \times 80}} = \frac{{17}}{{65}} \cr & \frac{x}{y} = \frac{{17}}{{65}} \times \frac{{16}}{{23}} = \frac{{272}}{{1495}} \cr} $$

Given
10% of the voters did not cast their vote and 10% of the polled vote were found invalid
The winner candidate got 54% of the valid vote and beat the opposition by 1620 votes
Concept used:
The percentage is calculated as based on 100 i.e. 100 is the base
40% means 40 out of 100
Calculation:
Let, total enrolled voter be $$x$$
10% did not cast vote means casted or polled vote = $$\frac{{9x}}{{10}}$$
10% vote is invalid
That means valid vote = $$\frac{{90}}{{100}} \times \frac{{9x}}{{10}}$$
$$ \Rightarrow \frac{{81x}}{{100}}$$
The winner candidate got 54% of the polled vote means loosed got (100 - 54) = 46% vote
Winner candidate got total $$\left( {\frac{{54}}{{100}} \times \frac{{81x}}{{100}}} \right)$$   vote
And the looser candidate got $$\left( {\frac{{46}}{{100}} \times \frac{{81x}}{{100}}} \right)$$   vote
Accordingly,
$$\eqalign{ & \left( {\frac{{54}}{{100}} \times \frac{{81x}}{{100}}} \right) - \left( {\frac{{46}}{{100}} \times \frac{{81x}}{{100}}} \right) = 1620 \cr & \Rightarrow \left( {\frac{{81x}}{{100}}} \right) \times \left( {\frac{{54 - 46}}{{100}}} \right) = 1620 \cr & \Rightarrow \frac{{\left( {81 \times 8} \right)x}}{{10000}} = 1620 \cr & \Rightarrow x = \frac{{1620 \times 10000}}{{81 \times 8}} \cr & \Rightarrow x = 25000 \cr} $$
∴ Total 25000 voters registered in the voter list.

Let, number = x
40% of x + 30% of x = 70
70% of x = 70
x = 100

Given:
Registered voters for P supporters = 70%
60% of the P supporters and 30% of the Q supporters are expected to vote for candidate P.
Concept used:
Let total voters be 1000
Then 700 are P supporters and 300 are Q supporters
Total votes of P
⇒ 60% of 700 + 30% of 300
⇒ 420 + 90
⇒ 510
Percentage of P voters
⇒ $$510 \times \frac{{100}}{{1000}}$$
⇒ 51%
Hence, the required value is 51%