Percentage - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & {\text{Let numerator}} = 5x \cr & {\text{denominator}} = 5y \cr & {\text{So as per question}} \cr & \frac{{5x + 3x}}{{5y + 2y}} = \frac{{16}}{{23}} \to \frac{x}{y} = \frac{2}{9} \cr & {\text{So the original fraction}}\,\frac{{5x}}{{5y}} = \frac{2}{9} \cr} $$

Let C marks = 100

More = 120 - 90 = 30
More % $$ = \frac{{30}}{{90}} \times 100 = 33\frac{1}{3}\% $$

$$\eqalign{ & 90\% \to 216 \cr & 10\% \to 24 \cr & 100\% \to \boxed{240} \cr} $$

$$\eqalign{ & 8\% \to 480 \cr & 1\% \to 60 \cr & 100\% \to \boxed{6000} \cr} $$

Run by boundaries = 6 × 4 + 4 × 6 = 48
By running = 120 - 48 = 72
% = $$\frac{{72}}{{120}}$$ × 100 = 60%

\[\begin{array}{*{20}{c}} {{\text{Income}}}&{{\text{Expenditure}}}& = &{{\text{Saving}}} \\ \begin{gathered} 100 \hfill \\ \,\, \downarrow \hfill \\ 129 \hfill \\ \end{gathered} &\begin{gathered} 80 \hfill \\ \, \downarrow \hfill \\ 96 \hfill \\ \end{gathered} &{}&{\left. \begin{gathered} 20 \hfill \\ \, \downarrow \hfill \\ 33 \hfill \\ \end{gathered} \right)13} \end{array}\]
$$\frac{{13}}{{20}} \times 100 = 65\% $$

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Alternate Solution :

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First, let's assume Renu's initial income is Rs. 100 (we can pick any number, 100 makes the math easier).

If she saves 20%, her initial savings are 20% of Rs. 100 = Rs. 20.

Her initial expenditure is then Rs. 100 (income) - Rs. 20 (savings) = Rs. 80.

Now, her expenditure increases by 20%. So, the increase in expenditure is 20% of Rs. 80 = Rs. 16.

Her new expenditure is Rs. 80 + Rs. 16 = Rs. 96.

Her income also increases, by 29%. So, the increase in income is 29% of Rs. 100 = Rs. 29.

Her new income is Rs. 100 + Rs. 29 = Rs. 129.

Her new savings are now Rs. 129 (new income) - Rs. 96 (new expenditure) = Rs. 33.

To find the percentage increase in savings, we compare the new savings to the old savings.

The increase in savings is Rs. 33 (new savings) - Rs. 20 (old savings) = Rs. 13.

The percentage increase in savings is (Increase in savings / Original savings) * 100 = (Rs. 13 / Rs. 20) * 100 = 65%.

Therefore, her saving increases by 65%.

The correct answer is Option B: 65%.

Radius = 5 : 4
Height = 5 : 6
Volume = 5² × 5 : 4² × 6
         
Decrease % = $$\frac{{29}}{{125}}$$ × 100 = 2.23%

x% of 100 = (100 - x)
x = 100 - x
2x = 100
x = 50

$$\eqalign{ & 91\% {\text{ of }}A = 39\% {\text{ of }}B \cr & \frac{{91}}{{100}} \times A = \frac{{39}}{{100}} \times B \cr & B = \frac{{91}}{{39}}A \cr & B = x\% {\text{ of }}A \cr & \frac{{91}}{{39}} \times A = \frac{x}{{100}} \times A \cr & x = \frac{{91}}{{39}} \times 100 = \frac{{700}}{3} \cr} $$

$$\eqalign{ & {\text{Reduction of money}} = 450 \times \frac{{20}}{{100}} = 90 \cr & {\text{After reduction price}} = \frac{{90}}{{50}} = {\text{Rs}}{\text{. }}1.8{\text{ per kg}} \cr & {\text{Increase in price }}20\% = \frac{1}{5} \cr & {\text{4 unit}} = \frac{9}{5} \cr & {\text{1 unit}} = \frac{9}{{5 \times 4}} \cr & {\text{5 unit}} = \frac{9}{{5 \times 4}} \times 5 = \frac{9}{4} = {\text{Rs}}{\text{. }}2.25 \cr} $$