Percentage - Aptitude MCQ Questions and Solutions with Explanations

Let the number be x
According to the question,
91 - $$\frac{{30{\text{x}}}}{{100}}$$ = x
9100 - 30x = 100x
Or, 9100 = 130x
Or, x = $$\frac{{9100}}{{130}}$$
Hence, x = 70

100000 == 10%↑(1^st year) ==> 110000 == 10%↑(2^nd year) ==> 121000
Population at starting of 3^rd year = 121000

[By using net percentage change method, we have saved our self from cumber some formulas on population which is based on compound interest].

Let Ashu's salary = 100; Ashu's salary after rise = 125
Then Vicky's salary = 175
Vicky's salary after rise of 40% = 245
[As 10% of Vicky's salary is 17.5 then 40% = 17.5 × 4 = 70]

Difference between Vicky's salary and Ashu's salary = 245 - 125 = 120
% more Vicky's salary than Ashu's = $$\frac{{120 \times 100}}{{125}} = 96\% $$

Let there is 100 kg of ore.
25% ore contains 90% off Iron that means 25 kg contains;
$$\frac{{25 \times 90}}{{100}} = 22.5\,{\text{kg}}\,{\text{iron}}$$
22.5 kg Iron contains 100 kg of ore.
Then, 1 kg of iron contains = $$\frac{{25}}{{100}}{\text{kg}}\,{\text{ore}}$$
Hence, 60 kg iron contains
= $$\frac{{100 \times 60}}{{22.5}}$$
= 266.66 kg ore

Number of Indians men present there = $$\frac{{700 \times 20}}{{100}} = 140$$
Indian women = $$\frac{{500 \times 40}}{{100}} = 200$$
Indian children = $$\frac{{800 \times 10}}{{100}} = 80$$
Total member present in climate conference = 700 + 500 + 800 = 2000
Total Indian = 200 + 140 + 80 = 420
Hence, % of Indian present there = $$\frac{{420 \times 100}}{{2000}} = 21\% $$
% of people who were not Indian = 100 - 21 = 79%

Let 100 kg of hematite be obtained then 20% of it get wasted that means 80 kg of ore remains.
Pure iron = 25% of remaining ore = $$\frac{{80 \times 25}}{{100}} = 20\,{\text{kg}}$$
20 kg pure Iron is obtained from 100 of hematite
1 kg pure Iron is obtained from = $$\frac{{100}}{{20}}$$ hematite
Then, 80000 kg pure Iron is obtained from =$$\,\frac{{100}}{{20}} \times 80000 = \,$$    $$400000\,{\text{kg}}$$   hematite.

The total cost for the year
= 250000 + 2% of 2500000 + 2000
= Rs. 257000
For getting return of 15% he must earn
= $$\frac{{257000 \times 15}}{{100}}$$
= Rs. 38550 per year
Then, Monthly Rent
= $$\frac{{38550}}{{12}}$$
= Rs. 3212.5

Let Ram's salary be x
He spends on rent = 30% of x = $$\frac{{30{\text{x}}}}{{100}}$$
He spends on education = 30% from rest of the salary = $$\frac{{30 \times 70{\text{x}}}}{{100 \times 100}} = \frac{{21{\text{x}}}}{{100}}$$
He Spends on clothes = 24% of total salary = $$\frac{{24{\text{x}}}}{{100}}$$
Saving = 2500
Salary of ram = x
$$\eqalign{ & \frac{{30{\text{x}}}}{{100}} + \frac{{21{\text{x}}}}{{100}} + \frac{{24{\text{x}}}}{{100}} + 2500 = {\text{x}} \cr & {\text{or,}}\,\frac{{75x}}{{100}} = {\text{x}} - 2500 \cr & {\text{or,}}\,75{\text{x}} = 100{\text{x}} - 250000 \cr & {\text{or, }}100{\text{x}} - 75{\text{x}} = 250000 \cr & {\text{or, x}} = \frac{{250000}}{{25}} \cr & {\text{or, x}} = 10000 \cr & {\text{Ram's}}\,{\text{salary = Rs}}{\text{.}}\,10000 \cr} $$

Let x be the page required when report is retyped
Now, we can use work equivalence method
20 × 55 × 65 = 70 × 65 × x
Or, x = $$\frac{{20 \times 55 \times 65}}{{70 \times 65}}$$
Or, x = 15.70 = 16 pages.
Hence, % reduction in pages = $$\left( {20 - 16} \right) \times \frac{{100}}{{20}}$$   $$\, = \,$$ $$20\% $$

Let initial price of Maruti Car be Rs. 100
As price increases 30%, price of car will become, (100 + 30% of 100) = Rs. 130
Due to increase in price, sales is down by 20%. It means, it is going make 20% less revenue as expected after increment of price
So, New revenue = (130 - 20% of 130) = Rs. 104
The initial revenue was Rs. 100 which becomes Rs. 104 at the end. It means there is 4% increment in the total revenue

Mind Calculation Method:
100 == 30%↑(price effect) ==> 130 == 20%↓(sales effects) ==> 104
Hence, 4% rises