Let Rs. 100 be spend on rice initially for 20 kg. As the price falls by 20%, new price for 20 kg rice,= (100 - 20% of 100) = 80 New price of rice = $$\frac{{80}}{{20}}$$ = Rs. 4 per kg. Rice can bought now at = $$\frac{{100}}{{4}}$$ = 25 kg.

Winner gets 65% of valid votes and loser gets 35% of votes Difference between this two = 2748 (65-35)% = 2748 30% = 2748 Total number of voters, 100%
= $$\frac{{2748 \times 100}}{{30}}$$ = 9160

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

$$\eqalign{ & {\text{Let the present population of the town be }}P \cr & {\text{Using compound interest formula}} \cr & {\text{Then}}, \cr & P = x\left[ {1 + \left( {\frac{R}{{100}}} \right)} \right] - - - \,\left( i \right) \cr & {\text{And}}\,y = P\left[ {1 + \left( {\frac{R}{{100}}} \right)} \right] \cr & = P \times \frac{P}{x} - - - - \,\left( {ii} \right) \cr & {P^2} = xy; \cr & {\text{Hence}},\,P = \sqrt {xy} \cr} $$

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% = $$\frac{1}{3}$$

Let each side of the cuboid be 10 unit initially. Initial Volume of the cuboid, = length * breadth * height = 10 × 10 × 10 = 1000 cubic unit. After increment dimensions become, Length = (10 + 10% of 10) = 11 unit. Breadth = (10 + 20% of 10) = 12 unit. Height = (10 + 50% of 10) = 15 unit. Now, present volume = 11 × 12 × 15 = 1980 cubic unit. Increase in volume = 1980 - 1000 = 980 cubic unit. % increase in volume = $$\frac{{980}}{{1000}} \times 100 = 98\% $$ Mind Calculation Method: 100 == 50%↑(height effects) ==> 150 == 20%↑(breadth) ==> 180 == 10%↑(length effects) ==> 198 Change in volume = 98%
[We can take net percentage change in any order]

Narayan's saving and rent = 1000 + 1800 = Rs. 2800 Let his monthly income be Rs. 100 30% of his income he spent on education i.e. Rs. 30 Remaining = 100 - 30 = 70 50% of remaining on food = $$\frac{{70 \times 50}}{{100}} = {\text{Rs}}{\text{. 35}}$$ Now, that 35 must be equal to his saving and rent i.e. 35 = 2800 then, 1 = $$\frac{{2800}}{{35}}$$ 100 = $$\frac{{2800 \times 100}}{{35}} = {\text{Rs}}{\text{. 8000}}$$ So, his income = Rs. 8000

Let Q = 10. Then, P = 60. Q is 50 less than P. Q, % less than P = $$\frac{{50}}{{60}} \times 100 = 83.33\% $$ Alternative Method 10 (Q) == (6 times greater) ==> 60(P) == x%↓(Less than Q) ==> 10 (Q)
Now,
$${\text{x}} = \frac{{50 \times 100}}{{60}} = 83.33\% $$

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

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/br> 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, $$\eqalign{ & = \frac{{{\text{Actual}}\,{\text{Decrease}}\,{\text{in}}\,{\text{BC}}}}{{{\text{Original BC}}}} \times 100 \cr & = \frac{{0.18}}{2} \times 100 = 9\% \cr} $$

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

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.

$$\eqalign{ & {\text{Let number of men in the population be }}x \cr & {\text{Number of women}} = \left( {35000 - x} \right) \cr & {\text{Increase in the number of men}} \cr & = 6\% \,of\,x = \frac{{6x}}{{100}} \cr & {\text{Increase in the number of women}} \cr & = \left( {3500 - x} \right) \times \frac{4}{{100}} \cr & {\text{Increase in whole population}} \cr & = 36760 - 35000 = 1760 \cr & {\text{Now}}, \cr & \frac{{6x}}{{100}} + \left[ {\left( {35000 - x} \right) \times \frac{4}{{100}}} \right] = 1760 \cr & \left[ {\left( {6x - 4x} \right) + 35000 \times \frac{4}{{100}}} \right] = 1760 \cr & 2x + 35000 \times 4 = 1760 \times 100 \cr & 2x = 176000 - 35000 \times 4 \cr & x = 18000 \cr & {\text{Number}}\,{\text{of}}\,{\text{men}} = 18000 \cr & {\text{Number}}\,{\text{of}}\,{\text{women}} \cr & = 35000 - 18000 \cr & = 17000 \cr} $$

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%

Net percentage increase in Population = (2.5 - 0.5) = 2% each year. Let the Original Population of the town be 100. Population of Town after 1 year = (100 + 2% of 100) = 102. Population of the town after 2nd year = (102 + 2% of 102 ) = 104.04
Now, % increase in population = $$\frac{{4.04}}{{100}} \times 100 = 4.04\% $$ Mind Calculation Method: 100 == 2% Up(1st year) ==> 102 == 2%Up(2nd year) ==> 104.04 % population increase in 2 years = 4.04%.

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%.

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%

Let B's Salary is Rs. 100. Then, A's Salary = (100 + 25% of 100) = Rs. 125 Difference between A's Salary and B's Salary = 125 - 100 = Rs. 25 % Difference (lower) = $$\frac{{25}}{{125}} \times 100 = 20\% $$ Mind Calculation Method: 100(B salary) === 25%↑ ===> 125(A salary) === 20%↓ ===> 100 (B salary) B's salary is 20% lower than A's

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 third number be 100. Then,
1st number = 130
2nd number = 140
% 1st number to the 2nd number
$$\eqalign{ & = \frac{{130 \times 100}}{{140}} \cr & = \frac{{650}}{7} \cr & = 92\frac{6}{7}\% \cr} $$