Percentage - Aptitude MCQ Questions and Solutions with Explanations

Schedule working hours in week = 48
Total pay in a week for schedule working hours = Rs. 480
Pay per hour for schedule working hours = $$\frac{{480}}{{48}}$$ = Rs. 10
Pay per hour for over time = 10 + 25% of 10 = Rs. 12.5
Total pay in that particular week = Rs. 605
Extra pay = 605 - 480 = 125
So, total over time = $$\frac{{125}}{{12.5}}$$  = 10 hours
Thus, total work hour altogether in that week = 48 + 10 = 58 hours

Winner gets 55% of votes.
As 4% votes were declared invalid so 96% would be the valid votes
So,
Winner gets 55% of 96% valid votes
Winner gets % valid votes = $$\frac{{55 \times 96}}{{100}}$$   = 52.8% votes
Loser gets = 96 - 52.8 = 43.2% votes
Difference = 9.6%
Now, 9.6% = 4800
So, 1% = $$\frac{{4800}}{{9.66}}$$
Thus, 100% Votes = $$\frac{{4200 \times 100}}{{9.66}}$$   = 50000
Hence, Total Voters = 50000

Alternatively,
Let total number of voters were X
Invalid Votes = 4%
Valid Votes = 96%
Total Valid Votes = 96% of X = $$\frac{{96{\text{x}}}}{{100}}$$ = 0.96X
Winner gets 55% of Valid Votes,
$$ = \frac{{0.96 \times 55}}{{100}} = 0.528{\text{x}}$$      votes
Loser gets = (0.96X - 0.528X) = 0.432X
Difference = 0. 528 - 0.432 = 0.096X
0.096X = 4800
X = 50000

Money spent originally = Rs. 2160
Less money to be spent for now for the same length of cloth,
= 10% of 2160 = Rs. 216
It means Rs. 216 enables a man to buy 6 meters of cloth
So, reduced price = $$\frac{{216}}{6}$$ = Rs. 36 per meter
And the original price = $$\frac{{100 \times 36}}{{90}}$$   = Rs. 40 per meter

Let original area of the garden was 100 square unit.
Increase or decrease in area can be easily determined by this graphic:
100 == 40% up length ==> 140 == 20% down width ==> 112 (Final Area)
So, there is 12% increase in area of the garden.

Let B = 100 Then,
A = 100 + 40% of 100 = 140
Let C = X
X - 20% of X = 100
0.8X = 100
X = $$\frac{{100}}{{0.8}}$$ = 125
∴ A : C = $$\frac{{140}}{{125}}$$ = 28 : 25

Number of runs made by running
= 110 - (3 x 4 + 8 x 6)
= 110 - (60)
= 50
∴ Required percentage
$$\eqalign{ & = \left( {\frac{{50}}{{110}} \times 100} \right)\% \cr & = 45\frac{5}{{11}}\% \cr} $$

Let their marks be (x + 9) and x
Then,
$$\eqalign{ & x + 9 = \frac{{56}}{{100}}\left( {x + 9 + x} \right) \cr & \Rightarrow 25\left( {x + 9} \right) = 14\left( {2x + 9} \right) \cr & \Rightarrow 3x = 99 \cr & \Rightarrow x = 33 \cr} $$
So, their marks are 42 and 33

Suppose originally he had x apples
Then,
$$\eqalign{ & \left( {100 - 40} \right)\% \,{\text{of}}\,x = 420 \cr & \Rightarrow \frac{{60}}{{100}} \times x = 420 \cr & \Rightarrow x = {\frac{{420 \times 100}}{{60}}} = 700 \cr} $$

Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1.
Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such number = 14
$$ = \left( {\frac{{14}}{{70}} \times 100} \right)\% = 20\% $$

$$\eqalign{ & x\% \,{\text{of}}\,y = {\frac{x}{{100}} \times y} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\frac{y}{{100}} \times x} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = y\% \,{\text{of}}\,x \cr & \therefore A = B \cr} $$