Percentage - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & {\text{Required}}\,{\text{Percentage}} \cr & = \frac{{ {1.14 \times 100} }}{{1.9}} \cr & = 60\% \cr} $$

Students passed in English = 80%
Students passed in Math's = 85%
Students passed in both subjects = 73%
Then, number of students passed in at least one subject
= (80+85)-73
= 92%. [The percentage of students passed in English and Maths individually, have already included the percentage of students passed in both subjects. So, We are subtracting percentage of students who have passed in both subjects to find out percentage of students at least passed in one subject.]

Thus, students failed in both subjects = 100-92 = 8%.

$$\eqalign{ & {\text{As}}\,{\text{we}}\,{\text{know}},\,1\% = \frac{1}{{100}} \cr & {\text{Hence}},\, \cr & \frac{1}{2}\% = {\frac{1}{2} \times \frac{1}{{100}}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{1}{{200}} \cr & \,\,\,\,\,\,\,\,\,\,\, = 0.005 \cr} $$

Let the initial price of the commodity be 100.

After 50% increase in price, It will become,
100 ------50% increase----> 150.
Now, we have to reduce the consumption to keep expenditure 100.

Increase in price= 150 - 100 = 50
We have to reduce the consumption,
$$\eqalign{ & = \frac{{50}}{{150}} \times 100 \cr & = \frac{1}{3}{\text{ or 33}}{\text{.33}}\% \cr} $$

Other Method:
Here, we use, Final product constant graphic.
100 ==50% up== 150===33.33% down===>100
Consumption Reduce = 33.33% = $$\frac{1}{3}$$

Here we can use the compound interest based formula,
$$\eqalign{ & {\text{Population after }}n{\text{ years}} \cr & = P \times {\left[ {1 + {\frac{r}{{100}}} } \right]^n} \cr & {\text{Population after 2 years}} \cr & = 50000 \times {\left[ {1 + {\frac{4}{{100}}} } \right]^2} \cr} $$
Population after 2 years = 54080

Alternatively,
we can use, net percentage change graphic as well,
50,000------4%↑---→ 52,000---- 4%↑---→ 54,080.
Then, population after 2 years= 54,080.
In this calculation, we need to find 1% of 50,000 first, which is easily calculated by dividing 50,000 by 100.

As A and B are fixed, C is any point on AB, so if AC is increases then CB decreases.
A________3 cm_________ C _____2 cm____B
Then, solution can be visualized as,
Increase in AC 6% = $$\frac{{106 \times 3}}{{100}} = 3.18\,{\text{cm}}{\text{.}}$$
Decrease in CB = 0.18 cm
% decrease = $$\frac{{0.18}}{2} \times 100 = 9\% $$

Alternatively,
AC = 3 Cm.
BC = 2 Cm.
Increase in AC by 6%, then
New, AC = 3 + 6% of 3 = 3 + 0.18 = 3.18 cm.
0.18 cm increase in AC means 0.18 cm decrease in BC as already mentioned AB as the fixed point.
So, % decrease in BC,
$$\eqalign{ & = \frac{{{\text{Actual}}\,{\text{Decrease}}\,{\text{in}}\,{\text{BC}}}}{{{\text{Original BC}}}} \times 100 \cr & = \frac{{0.18}}{2} \times 100 = 9\% \cr} $$

Initial Cost = Rs. 75
After 20% increase in the cost, it becomes,
(75 + 20% of 75) = Rs. 90
Now, Cost is decreased by 20%, So cost will become,
(90 - 20% of 90) = Rs. 72
So, present cost is Rs. 72

Let the initial expenses on Sugar was Rs. 100.
Now, Price of Sugar rises 25%. So, to buy same amount of Sugar, they need to expense,
= (100 + 25% of 100) = Rs. 125.
But, They want to keep expenses on Sugar, so they have to cut Rs. 25 in the expenses to keep it to Rs. 100.
Now, % decrease in Consumption,
$$\frac{{25}}{{125}} \times 100 = 20\% $$

Mind Calculation Method;
100 === 25%↑ ===> → 125 === X%↓ ===> 100
Here, X = $$\frac{{25}}{{125}} \times 100 = 20\% $$

Let the Original length of the rectangle be 20 unit and breadth be 10 unit. Then
Original Area = length *breadth = 20*10 = 200 Square unit.
40% decrease in each side, then
Length = (20 - 40% of 20) = 12 unit.
Breadth = (10 - 40% of 10) = 6 unit.
Now, Area = 12 × 6 = 72 Square unit.
Decrease in area = 200 - 72 = 128 square unit.
% Decrease in Area = $$\frac{{128}}{{200}} \times 100 = 64\% $$

Mind Calculation Method:
Let the original area be 100 square unit.
100 === 40%↓(decrease in length) ==⇒ 60 === 40%↓ === (decrease in breadth) ===> 36
Diminished in area = 100 - 36 = 64%

Let the initial expenditure on the commodity be Rs. 100.
Now, the price decreases by 20%,
Current Price = (100 - 20% of 100) = Rs. 80.
Same time due to decrements in price 20% consumption has been increased. So,
Current expenses on commodity = (80 + 20% of 80)= Rs. 96.
Here, the initial expenditure was Rs. 100 which became 96 at the end, it means there is 4% decrements in the expenditure of the commodity.

Mind Calculation Method:
100 === 20%↓(Decrements in Price) ===> 80 === 20%↑(Increment in Consumption) ===> 96.
Thus, there is a decrements of 4%