Percentage - Aptitude MCQ Questions and Solutions with Explanations

\[\begin{array}{l} 75 \to \frac{3}{4}\\ \begin{array}{*{20}{c}} {{\rm{Income}}}&{}&{{\rm{Expenditure}}}&{{\rm{Saving}}}\\ {400}&{}&{300}&{100}\\ {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \downarrow + 28\% }&{}&{\,\,\,\,\,\,\,\,\,\,\,\,\, \downarrow + 20\% }& \downarrow \\ {112}& - &{60}&{ = 52\% } \end{array}\\ {\rm{Saving}} = 52\% \end{array}\]

Given:
A, B, and C spend 80%, 85%, and 75% of their incomes respectively.
Savings are in the ratio 8 : 9 : 20 respectively.
Difference between the income of A and C is Rs. 18,000.
Concept used:
Income - Expenditure = Savings
Calculation:
A, B and C spend 80%, 85% and 75% of their incomes respectively.
Out of 100%, A spend 80%,
Income : Expenditure = 100 : 80 = 5 : 4,
Out of 100%, B spend 85%,
Income : Expenditure = 100 : 85 = 20 : 17,
Out of 100%, C spend 75%,
Income : Expenditure = 100 : 75 = 4 : 3,
Ratio Income : Expenditure is 5 : 4, 20 : 17, 4 : 3 respectively.
Savings = Income - Expenditure
Savings of A : B : C = (5 - 4) : (20 - 17) : (4 - 3)
Savings of A : B : C = 1 : 3 : 1
According to the question,
Savings are in the ratio 8 : 9 : 20 respectively.
Adjusting the savings ratio,
⇒ Savings = 1 × 8 : 3 × 3 : 1 × 20 = 8 : 9 : 20
⇒ Income = 5 × 8 : 20 × 3 : 4 × 20 = 40 : 60 : 80
⇒ Expenditure = 4 × 8 : 17 × 3 : 3 × 20 = 32 : 51 : 60
According to the question,
Income of C - Income of A = 18,000
⇒ 80 - 40 = 18,000
⇒ 1 unit = $$\frac{{18,000}}{{40}}$$  = 450
Income of B = 60 unit
⇒ 60 × 450 = Rs. 27,000
∴ The income of B is Rs. 27,000.

$$\eqalign{ & {\text{Let initial amount}} = n \cr & \frac{{n \times 160}}{{100}} \times \frac{{50}}{{100}} \times \frac{{160}}{{100}} \times \frac{{50}}{{100}} \times \frac{{160}}{{100}} \times \frac{{50}}{{100}} = 15360 \cr & \frac{{n \times 16}}{{10}} \times \frac{1}{2} \times \frac{{16}}{{10}} \times \frac{1}{2} \times \frac{{16}}{{10}} \times \frac{1}{2} = 15360 \cr & \frac{{512n}}{{10 \times 10 \times 10}} = 15360 \cr & n = 30,000 \cr} $$

$$\eqalign{ & = 2 \times 1500 \times \frac{{88}}{{100}} \times \frac{{19}}{{20}} \cr & = {\text{Rs}}{\text{. }}2508 \cr} $$

$$\eqalign{ & {\text{Richa : Rita}} \cr & \,\,\,\,\,100:85 \cr & {\text{Increase}}\% = \frac{{\left( {100 - 85} \right)}}{{85}} \times 100 \cr & = \frac{{15}}{{85}} \times 100 \cr & = 17\frac{{11}}{{17}}\% \cr} $$

$$\eqalign{ & 10\% = \frac{1}{{10}},\,A\% = \frac{A}{{100}},\,20\% = \frac{1}{5} \cr & 45000 \times \frac{{11}}{{10}} \times \frac{{100 + A}}{{100}} \times \frac{6}{5} = 83160 \cr & 100 + A = 140 \cr & A = 40 \cr} $$

Let, weekly income =

⇒ 6μ → 40
⇒ 24μ → 160 Answer

Total number of votes = 5x
Votes polled = 4x
Valid votes = 4x - 82560
Invalid votes = 82560
Defeated candidate = 42% of valid votes
Winning n = 58% of valid votes
16% of valid votes (difference) = 768400
16%(4x - 82560) = 768400
4x = 4802500 + 82560
x = 1221265
$$\eqalign{ & {\text{Required}}\% = \frac{{{\text{Invalid votes}}}}{{{\text{Number of people not voted}}}} \times 100 \cr & = \frac{{82560}}{{1221265}} \times 100 \cr & = 6.76\% \cong 6.8\% \cr} $$

Alternate solution
Given:
Number is first increased by 40% and then decreased by 25%, again increased by 15% and then decreased by 20%
$$\eqalign{ & {\bf{Calculation:}} \cr & {\text{Let the number be }}x \cr & \Rightarrow x \times \frac{7}{5} \times \frac{3}{4} \times \frac{{23}}{{20}} \times \frac{4}{5} \cr & \Rightarrow x \times \frac{{483}}{{500}} \cr & \Rightarrow 0.966x \cr & \Rightarrow 0.966x{\text{ is less than }}x \cr & \Rightarrow {\text{Decrease percent in the number}} \cr & = \frac{{x - 0.966x}}{{100}} \cr & = 3.4\% \cr & \therefore {\text{Net decrease percent in the number is }}3.4\% \cr} $$

$$\eqalign{ & \frac{{25\% \,{\text{of}}\left( {50\% \,{\text{of }}30\% \,{\text{of }}150} \right)}}{{40\% \,{\text{of }}2250}} \cr & = \frac{{25\% \times \left( {50\% \times 30\% \times 150} \right)}}{{40\% \times 2250}} \cr & = \frac{{25}}{{40}}\% \cr & = 0.625\% \cr} $$