Percentage - Aptitude MCQ Questions and Solutions with Explanations

Let us assume there are 100 students in the institute.
Then, number of boys = 60
And, number of girls = 40
Further, 15% of boys get fee waiver = 9 boys
7.5% of girls get fee waiver = 3 girls
Total = 12 students who gets fee waiver
But, here given 90 students are getting fee waiver. So we compare
12 = 90
So, 1 = $$\frac{{90}}{{12}}$$ = 7.5
Now number of students who are not getting fee waiver = 51 boys and 37 girls
50% concession = 25.5 boys and 18.5 girls (i.e. total 44)
Hence, required students = 44 × 7.5 = 330

We solve it through options. Choosing options for trial depends on mental thought.
100 == 12% up ==> 112 == 12% up ==> 125.44 == 12% Up ==> 140.49
So, answer is 12%

Let the marks obtained in five subjects be 6x, 7x, 8x, 9x and 10x.
Total marks obtained = 40x
Max. Marks of the five subjects = $$\frac{{40{\text{x}}}}{{0.6}}$$   [40x is 60% of total marks]
Max. Marks in each subject = $$\frac{{40{\text{x}}}}{{0.6 \times 5}}$$   = 13.33x
Hence, % of each subject = $$\frac{{6{\text{x}} \times 100}}{{13.33}}$$   = 45.01%
Or, $$\frac{{7{\text{x}} \times 100}}{{13.33}}$$   = 52.51
In same way other percentage are 60.01%, 67.52%, 75.01%.
Hence, number of subjects in which he gets more than 50% marks = 4

Let length, breadth and height of the room be 3, 2, 1 unit respectively.
Area of walls = 2(l + b) × h = 2(3 + 2) × 1 = 10 sq. unit.
Now, length, breadth and height of room will become 6, 1 and $$\frac{1}{2}$$ respectively.
Now, area of walls = $$2\left( {6 + 1} \right) \times \frac{1}{2}$$   = 7 sq. unit.
% decrease in the area of walls = $$\left( {10 - 7} \right) \times \frac{{100}}{{10}}$$   = 30%

Let the number of bacteria in the 1^st generation be x, then number of bacteria in 2^nd, 3^rd, 4^th . . . . . Generation would be
$$8\left( {\frac{{\text{x}}}{2}} \right),\,8\left( {\frac{{4{\text{x}}}}{2}} \right),\,8\left( {\frac{{16{\text{x}}}}{2}} \right)$$     . . . . And so on.
As x, 4x, 16x, 64x . . . . . it is in GP with common ratio 4
Hence, 7th term of GP,
x(4)⁶ = 4096
or, x = 1 or 1 million.

Increase in the price of sugar = (8 + 2) = 10%
Hence, price of sugar on, Jan. 1, 1996
$$\eqalign{ & = \frac{{20 \times 110 \times 110}}{{100 \times 100}} \cr & = {\text{Rs}}{\text{.}}\,24.20 \cr} $$

Passed in none = 5%
Passed in all = 5%
Passed in four = 20% of 90% = 18%
Passed in one = 25% of 90% = 22.5%
Passed in two = 24.5%
Passed in three = (100 - 5 - 5 - 22.5 - 24.5 - 18) = 25%
But given 300 students passed in three
Hence, 25% = 300
So, 100% = 1200
1200 students must have appeared

Time lost over two weeks = 25% a week time(given that $$\frac{1}{2}$$ % clock loses in first week and in the second week it gains $$\frac{1}{4}$$ % on true time)
A week = 168 hours
Hence, clock lost = 0.42 hours = 25.2 minutes or 25 minute 12 seconds
Thus, correct time = 11 : 34 : 48

$$\eqalign{ & {\text{Shrinking of cloth}}, \cr & = {\frac{{ {36 - 33} }}{{36}}} \times 100 \cr & = \frac{{100}}{{12}}\% \cr & {\text{Second time the strip shrinks,}} \cr & = \frac{{ {48 \times 100} }}{{1200}} \cr & = 4\,\text{inches} \cr & {\text{hence,}}\,{\text{the}}\,{\text{cloth}}\,{\text{remains}} \cr & = 48 - 4 \cr & = 44 \cr} $$

$$\eqalign{ & {\text{According}}\,{\text{to}}\,{\text{question,}} \cr & {\frac{{XY}}{{100}}} + {\frac{{YX}}{{100}}} \cr & = \frac{{2XY}}{{100}} \cr & = 2\% \,of\,XY \cr} $$