Percentage - Aptitude MCQ Questions and Solutions with Explanations

20 litres juice contain 10% Tomato, i.e.
20L juice = $$\frac{{20 \times 10}}{{100}}$$  = 2L Tomato
Tomato puree contains 80% of water and 20% tomato.
This 80% tomato = 2L (which is contained by 100 puree)
So, Now this 2 L Consist 80% in puree
Thus, total puree will be $$\frac{2}{{.8}} = 2.5{\text{L}}$$

If we take different values of x then,
Let x = 150, then error%
$$\eqalign{ & = \frac{{ {\frac{{ {200 - 100} }}{{100}}} }}{{100}} \cr & = 100\% \cr} $$
Again if x = 100, then error%
$$\eqalign{ & = \frac{{ {\left( {150 - 50} \right) \times 100} }}{{100}} \cr & = 200\% \cr} $$
If we take different value of x,
we get different answer so we can't determine it.

Total student = 100
Boys = 60
Girls = 40
Boys who plays hockey = 40% = 24
There is no information about boys who play badminton.
Girls who plays Badminton = 75% = 30
No girls plays hockey.
Since, we do not have information that whether the rest of the boys are playing badminton or not. So, we cannot determine the total no. of student who don't play any game.

$$\eqalign{ & {\text{Let the required number of pages be }}x. \cr & 30 \times 25 \times 35 = x \times 30 \times 28 \cr & x = 31.25 \approx 32 \cr & \% \,{\text{increase}}\,{\text{in}}\,{\text{number}}\,{\text{of}}\,{\text{pages}}, \cr & = {\frac{2}{{30}}} \times 100 \cr & = 6.66\% \cr} $$

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{fraction}}\,{\text{be}}\,\frac{{100x}}{{100y}} \cr & {\text{Now}}\,{\text{according}}\,{\text{to}}\,{\text{the}}\,{\text{question}}, \cr & {\left( {\frac{{100x}}{{100y}}} \right)^2} = \frac{{125{x^2}}}{{80{y^2}}} = \frac{{25{x^2}}}{{16{y^2}}} \cr & \frac{{25{x^2}}}{{16{y^2}}} = \frac{5}{8}\left( {\frac{{100x}}{{100y}}} \right) \cr & {\frac{{100x}}{{100y}}} = \frac{2}{5} \cr & {\text{hence}}, \cr & {\text{product of numerator and denominator}} \cr & = 2 \times 5 = 10 \cr} $$

Let X be the number which is added to 80
80% of X = 0.8X
Now,
80 + 0.8X = X
0.2X = 80
X = $$\frac{{80}}{{0.2}} = 400$$

$$\eqalign{ & {\text{Reduction}} \cr & = {\frac{7}{{107}}} \times 2568 \cr & = 168 \cr} $$

Since,
Run scored = Over × Run rate
If overs is reduced by 25%, run rate will go up by 33.33%. Hence, Australia could have scored any number of runs.

In 2000, the market share was 40%, 30% and 30%, means
the ratio is 4 : 3 : 3
In 2001, a new product (A) enters and has 10% market share, 90% of the remaining market is shared by the previous 3.
Now, divide 90% in the ratio 4 : 3 : 3 , i.e 36%, 27%, 27%.
Now the ratio is 36 : 27 : 27 : 10
In 2002, another new product (B) enters and has 10% market share, now the remaining 90% market share is distributed in the ratio,
36 : 27 : 27 : 10
and hence remaining 32.4%, 24.3%, 24.3%, 9%
Thus, the market share of Margo in 2002 is 32.4%

$$\eqalign{ & {\text{Let the total number of applicants be x}}. \cr & {\text{Number of eligible candidates}} \cr & = {\text{ }}95\% {\text{ }}of{\text{ }}x \cr & {\text{Eligible candidates of other categories}}, \cr & = 15\% \,of\,\left( {95\% {\text{ }}of{\text{ }}x} \right) \cr & = {\frac{{15}}{{100}}} \times {\frac{{95}}{{100}}} \times x \cr & = \frac{{57}}{{400}}x \cr & or,\left( {\frac{{57}}{{400}}} \right)x \cr & x = \frac{{ {4275 \times 400} }}{{57}} \cr & \,\,\,\,\,\, = 30000 \cr} $$