All questions of Percentages for Class 10 Exam

Calculation of Total Duty

- Wood A: 15% of Rs. 440000 = Rs. 66000
- Wood B: 9% of Rs. 230000 = Rs. 20700
- Wood C: 7% of Rs. 190000 = Rs. 13300

Total Duty:
- Rs. 66000 + Rs. 20700 + Rs. 13300 = Rs. 100000

Therefore, the total duty that the company had to pay on all items is Rs. 100000. This makes option 'b' the correct answer.

To find the total votes cast in the election, we need to determine the valid votes and the percentage of invalid votes.

Let's assume the total votes cast in the election as 'x'.

Invalid Votes:
Given that 20% of the votes cast in the election are invalid, we can calculate the number of invalid votes as:
20% of x = (20/100) * x = 0.2x

Valid Votes:
The valid votes can be calculated by subtracting the number of invalid votes from the total votes cast:
Valid votes = Total votes cast - Invalid votes
Valid votes = x - 0.2x = 0.8x

Candidate A's Votes:
Candidate A got 54% of valid votes, so the number of votes received by Candidate A can be calculated as:
54% of valid votes = (54/100) * 0.8x = 0.432x

Candidate B's Votes:
Since Candidate A won by 3200 votes, we can calculate Candidate B's votes as:
Candidate B's votes = Candidate A's votes - 3200
Candidate B's votes = 0.432x - 3200

Given that Candidate A won the election, Candidate B's votes must be less than Candidate A's votes. So we can write the equation:
0.432x - 3200 <>

Simplifying the equation, we find:
-3200 <>

Since the inequality -3200 < 0="" holds="" true="" for="" all="" values="" of="" x,="" there="" are="" no="" restrictions="" on="" the="" value="" of="" x.="" therefore,="" we="" can="" conclude="" that="" the="" total="" votes="" cast="" in="" the="" election="" can="" be="" any="" positive="">

Hence, the correct answer cannot be determined based on the given information.

To solve this problem, let's break it down into steps:

Step 1: Let's assume Kamal's monthly income is $100.
Step 2: Kamal saves x% of her monthly income, so her monthly savings would be x% of $100, which is $x.
Step 3: When her monthly expenditure is increased by 20%, her new monthly expenditure would be 100% + 20% = 120% of the original expenditure.
Step 4: When her monthly income is increased by 26%, her new monthly income would be 100% + 26% = 126% of the original income.
Step 5: When her monthly savings increase by 60%, her new monthly savings would be 100% + 60% = 160% of the original savings.

Now, let's calculate the new values:
New monthly expenditure = 120% of the original expenditure = 120/100 * $100 = $120
New monthly income = 126% of the original income = 126/100 * $100 = $126
New monthly savings = 160% of the original savings = 160/100 * $x = $1.6x

Since we know that Kamal's monthly savings increased by 60%, we can set up the equation:
$1.6x = $x + 60

Simplifying the equation, we get:
$1.6x - $x = 60
$0.6x = 60
x = 60 / $0.6
x = 100

Therefore, the value of x is 100.

However, none of the given answer options match the calculated value. So the correct answer is not provided in the options given.

Calculation of Concentration of the Solution:

- Mass of common salt = 33g
- Mass of water = 320g

Mass Percentage Formula:
Mass percentage = (Mass of solute / Mass of solution) * 100

Calculate the Mass Percentage:
Mass percentage = (33g / (33g + 320g)) * 100
Mass percentage = (33g / 353g) * 100
Mass percentage = 9.35%

Therefore, the concentration in terms of mass, by mass percentage of the solution is 9.35%.

Explanation:
The mass percentage of a solution represents the amount of solute present in a given amount of solution. In this case, the solution contains 33g of common salt in 320g of water. By using the mass percentage formula, we calculated that the concentration of the solution is 9.35%. This means that 9.35% of the solution is made up of common salt.

Given Information:
- Two numbers are 50% and 75% lesser than a third number.

Let's assume the third number is x.

Calculating the First Number:
- The first number is 50% lesser than x.
- Therefore, the first number is x - (50% of x) = x - 0.5x = 0.5x.

Calculating the Second Number:
- The second number is 75% lesser than x.
- Therefore, the second number is x - (75% of x) = x - 0.75x = 0.25x.

Calculating the Percentage Increase:
- To make the second number equal to the first number, we need to find the percentage increase required.
- Let's assume the percentage increase needed is y%.

The formula to calculate the percentage increase is given by:
Percentage Increase = (Increase in value / Original value) * 100

In this case, the increase in value is 0.5x - 0.25x = 0.25x.

Therefore, the equation becomes:
y = (0.25x / 0.25x) * 100
y = 100

Hence, the second number needs to be enhanced by 100% to make it equal to the first number.

Therefore, the correct answer is option 'D'.

To solve this problem, let's assume the number we are looking for is 'x'.

We are given that the difference between 41% of the number and 33% of the number is 960. Mathematically, this can be represented as:

(41/100)x - (33/100)x = 960

Simplifying the equation, we get:

(8/100)x = 960

Now, we need to find the value of 33.33% of the number, which can be calculated by multiplying the number by 33.33/100, or simply 0.3333.

So, the value of 33.33% of the number is:

(0.3333)x

To find the value of 'x', we can use the equation we derived earlier:

(8/100)x = 960

Multiplying both sides of the equation by 100/8, we get:

x = (960 * 100) / 8

Simplifying further, we have:

x = 12000

Now, substituting the value of 'x' in the expression for 33.33% of the number, we get:

(0.3333)(12000) = 3999.6

Since the question asks for the value to be rounded to the nearest whole number, we can round 3999.6 to 4000.

Therefore, the value of 33.33% of the number is 4000.

Hence, the correct answer is option C) 4000.

Let's assume the number is 'x'.

Given that 65% of the number is more than 25% of the number by 120, we can write the equation as follows:

0.65x - 0.25x = 120

Simplifying the equation, we get:

0.4x = 120

Now, let's solve for 'x':

x = 120 / 0.4
x = 300

So, the number is 300.

Now, we need to find 20% of this number.

20% of 300 can be calculated as:

(20/100) * 300 = 0.2 * 300 = 60

Therefore, 20% of the number is 60.

Hence, the correct answer is option 'A' - 60.

Given Data:
- A received 55% of the total votes
- B received the remaining votes
- If 10,000 votes from A were given to B, there would have been a tie

Let's solve the problem step by step:

Step 1: Setting up the equation
Let the total number of votes be x. Since A received 55% of the votes, the number of votes A received = 0.55x. The number of votes B received = x - 0.55x = 0.45x.

If 10,000 votes from A were given to B, the number of votes B received will be 0.45x + 10,000.

According to the given information, the number of votes A and B received after the transfer would be equal. Therefore, we can set up the equation:
0.55x - 10,000 = 0.45x + 10,000

Step 2: Solving the equation
0.55x - 0.45x = 10,000 + 10,000
0.1x = 20,000
x = 20,000 / 0.1
x = 200,000

Therefore, the total number of votes polled in the election is 200,000.

Conclusion:
The correct option is c) 200,000.

Given:
Initial price of petrol = Rs. 40 per litre
Final price of petrol = Rs. 60 per litre

To find:
The percentage by which a person has to decrease his consumption so that his expenditure remains the same.

Solution:
Let's assume that initially the person was consuming 'x' litres of petrol.

Initial Expenditure:
Initial price of petrol = Rs. 40 per litre
Initial consumption = 'x' litres
Initial expenditure = 40 * x = 40x

Final Expenditure:
Final price of petrol = Rs. 60 per litre
Final consumption = 'y' litres (to be determined)
Final expenditure = 60 * y = 60y

According to the given information, the person wants to keep his expenditure the same. So, we can equate the initial and final expenditures.

40x = 60y

Now, let's solve this equation for 'y' in terms of 'x' to find the final consumption.

Solving for y:
40x = 60y
Divide both sides by 60:
(40x)/60 = y
(2x)/3 = y

This equation tells us that the final consumption 'y' is equal to (2x/3). It means that the person needs to decrease his consumption by (x - (2x/3)) or (x/3) litres.

Percentage decrease in consumption:
The percentage decrease in consumption can be calculated using the formula:

Percentage decrease = (Decrease in consumption/Initial consumption) * 100

In this case, the decrease in consumption is (x/3) and the initial consumption is 'x'. So,

Percentage decrease = ((x/3)/x) * 100 = (1/3) * 100 = 33.33%

Therefore, the person needs to decrease his consumption by 33.33% in order to keep his expenditure the same. Hence, the correct answer is option C, 33.33%.

To solve this problem, we can break it down into smaller steps and use algebraic equations to find the answer.

Let's assume the number is represented by "x".

1. Calculate the average:
The average of the number, 50% of that number, and 25% of the same number is given as 280. So, we can write the equation as:
(x + 0.5x + 0.25x) / 3 = 280

2. Simplify the equation:
Combining like terms in the numerator, we get:
(1.75x) / 3 = 280

3. Solve for x:
To solve for x, we can multiply both sides of the equation by 3 to eliminate the fraction:
1.75x = 3 * 280

Now, we can simplify the right side of the equation:
1.75x = 840

Finally, divide both sides of the equation by 1.75:
x = 840 / 1.75

4. Calculate the value of x:
Evaluating the right side of the equation, we get:
x ≈ 480

Therefore, the number is approximately 480.

Hence, the correct answer is option B, 480.

Given information:
- There were two candidates in an election.
- 10% of voters did not vote.
- 48 votes were found invalid.
- The winning candidate got 53% of all the voters in the list and won by 304 votes.

To find: The total number of votes enrolled.

Solution:
Let's assume the total number of votes enrolled as 'x'.

Step 1: Calculate the number of voters who did not vote:
10% of voters did not vote, so the number of voters who did not vote is 10% of 'x', which can be written as:
Number of voters who did not vote = (10/100) * x

Step 2: Calculate the number of valid votes:
48 votes were found invalid, so the number of valid votes is 'x' minus the number of invalid votes, which can be written as:
Number of valid votes = x - 48

Step 3: Calculate the number of votes received by the winning candidate:
The winning candidate got 53% of all the voters in the list, so the number of votes received by the winning candidate is 53% of 'x', which can be written as:
Number of votes received by the winning candidate = (53/100) * x

Step 4: Calculate the number of votes received by the losing candidate:
The losing candidate received the remaining votes, which can be calculated as:
Number of votes received by the losing candidate = Number of valid votes - Number of votes received by the winning candidate

Step 5: Calculate the margin of victory:
The winning candidate won by 304 votes, so the margin of victory is 304.

Step 6: Set up an equation:
According to the given information, the margin of victory is equal to the difference between the votes received by the winning and losing candidates. So we can set up the following equation:
(Number of votes received by the winning candidate) - (Number of votes received by the losing candidate) = Margin of victory

Step 7: Solve the equation:
Substituting the values calculated in the previous steps, we can solve the equation to find the value of 'x':
(53/100) * x - (Number of valid votes - (53/100) * x) = 304

Simplifying the equation, we get:
(53/100) * x - (x - 48 - (53/100) * x) = 304
(53/100) * x - x + 48 + (53/100) * x = 304
(106/100) * x - x + 48 = 304
(6/100) * x = 304 - 48
(6/100) * x = 256

Simplifying further, we get:
(6/100) * x = 256
x = (256 * 100) / 6
x = 4266.67

Since the total number of votes enrolled should be a whole number, the nearest whole number to 4266.67 is 4267.

Therefore, the total number of votes enrolled is 4267, which is not provided as an option.

Conclusion:
Since