Percentage - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & {\text{Let,}} \cr & B = 110\% {\text{ of }}b = \frac{{11b}}{{10}}{\text{ }} \cr & C = 110\% {\text{ of }}c = \frac{{11c}}{{10}} \cr & D = 110\% {\text{ of }}d = \frac{{11d}}{{10}} \cr & {\text{Then,}} \cr & A = B \times \frac{D}{C} \cr & A = \frac{{11b}}{{10}} \times \frac{{11d}}{{10}} \times \frac{{10}}{{11c}} \cr & A = \frac{{11bd}}{{10c}} \cr & A = \frac{{11}}{{10}}a \cr & A = \frac{{110}}{{100}}a \cr & A = 110\% {\text{ of }}a \cr & \therefore {\text{ Increase }}\% = 10\% \cr} $$

Number of toffees distributed :
= 5% of 160 + 15% of 160 + $$\frac{{1}}{{4}}$$ of 160
= $$ \left( {\frac{5}{{100}} \times 160} \right) + \left( {\frac{{15}}{{100}} \times 160} \right) + $$      $$\left( {160 \times \frac{1}{4}} \right)$$
= 8 + 24 + 40
= 72
∴ Number of toffees left behind :
= 160 - 72
= 88

$$\eqalign{ & a = 60\% {\text{ of }}b \cr & \Rightarrow a = \frac{{60}}{{100}}b \cr & \Rightarrow b = \frac{5}{3}a \cr} $$
∴ Required percentage :
$$\eqalign{ & = \left( {\frac{{5b}}{{4a}} \times 100} \right)\% \cr & = \left( {5 \times \frac{5}{3}a \times \frac{1}{{4a}} \times 100} \right)\% \cr & = \left( {\frac{{625}}{3}} \right)\% \cr} $$

$$\left( {0.85\% {\text{ of }}405} \right) + \left( {2.25\% {\text{ of }}550} \right)$$
$$ = \left( {\frac{{85}}{{100}} \times \frac{1}{{100}} \times 405} \right) + $$     $$\left( {\frac{{225}}{{100}} \times \frac{1}{{100}} \times 550} \right)$$
$$\eqalign{ & = \frac{{225}}{{10000}}\left( {153 + 550} \right) \cr & = \left( {\frac{{225 \times 703}}{{10000}}} \right) \cr & = 15.8175 \cr} $$

Quantity of gold in the alloy :
= 80% of 50 g
= $$\left( {\frac{{80}}{{100}} \times 50} \right)$$  g
= 40 g
Let x g of gold be added
Then,
$$\eqalign{ & \Rightarrow \frac{{40 + x}}{{50 + x}} = \frac{{90}}{{100}} \cr & \Rightarrow \frac{{40 + x}}{{50 + x}} = \frac{9}{{10}} \cr & \Rightarrow 400 + 10x = 450 + 9x \cr & \Rightarrow x = 50 \cr} $$

Let the number be x
Then,
$$\eqalign{ & \Rightarrow \frac{1}{8}x = 41.5 \cr & \Rightarrow x = 41.5 \times 8 \cr & \Rightarrow x = 332 \cr & \therefore 69\% \,\,{\text{of}}\,\,332 \cr & = \left( {\frac{{69}}{{100}} \times 332} \right) \cr & = 229.08 \cr} $$

Total annual rent :
= Rs. (25000 × 12)
= Rs. 300000
Discount :
= 5% of Rs. 300000
= Rs. $$\left( {\frac{5}{{100}} \times 300000} \right)$$
= Rs. 15000
∴ Annual rent paid after discount :
= Rs. 300000 - 15000
= Rs. 285000

$$\left( {0.56\% \,\,{\text{of}}\,\,255} \right) \times $$   $$\left( {3.25\% \,\,{\text{of}}\,\,430} \right)$$
$$ = \left( {\frac{{56}}{{100}} \times \frac{1}{{100}} \times 225} \right) \times $$     $$\left( {\frac{{325}}{{100}} \times \frac{1}{{100}} \times 430} \right)$$
$$\eqalign{ & = \left( {\frac{{126}}{{100}} \times \frac{{13975}}{{1000}}} \right) \cr & = 1.26 \times 13.975 \cr & = 17.6085 \cr} $$

Correct time :
= 3 hrs 40 min
= (3 × 60 + 40) min
= 220 min
Error = 5.5 min
Error % :
= $$\left( {\frac{{5.5}}{{220}} \times 100} \right)$$  %
= $$\frac{5}{2}$$ %
= 2.5%

Let the number be x
Then,
$$\eqalign{ & \left( {100 + 37\frac{1}{2}} \right)\% \,\,{\text{of}}\,\,x = 33 \cr & \Rightarrow 137\frac{1}{2}\% \,\,{\text{of}}\,\,x = 33 \cr & \Rightarrow \frac{{275}}{2} \times \frac{1}{{100}} \times x = 33 \cr & \Rightarrow x = \left( {\frac{{33 \times 2 \times 100}}{{275}}} \right) \cr & \Rightarrow x = 24 \cr} $$