Frequently Asked Questions and Answers

Oct 13, 2025 by windailys.com 58 views

COMPETITIVE MODULE CLASS VIII 13. ARITHMETIC REASONING WORKSHEET - 1

The Ratio of number of boys and Girls in a school is 2:3. If 30% of Girls is "6" more than the 30% of Boys, then find the total number of students in the school?

Understanding the Problem

The problem presents a scenario where the ratio of boys to girls in a school is 2:3. This means that for every 2 boys, there are 3 girls in the school. The problem also states that 30% of the girls is 6 more than 30% of the boys. We need to use this information to find the total number of students in the school.

Breaking Down the Information

Let's break down the information given in the problem:

The ratio of boys to girls is 2:3.
30% of the girls is 6 more than 30% of the boys.

We can represent the number of boys as 2x and the number of girls as 3x, where x is a constant.

Using Algebra to Solve the Problem

Let's use algebra to solve the problem. We can start by representing the number of boys and girls in terms of x:

Number of boys = 2x
Number of girls = 3x

We are given that 30% of the girls is 6 more than 30% of the boys. We can represent this as an equation:

0.3(3x) = 0.3(2x) + 6

Simplifying the equation, we get:

0.9x = 0.6x + 6

Subtracting 0.6x from both sides, we get:

0.3x = 6

Dividing both sides by 0.3, we get:

x = 20

Finding the Total Number of Students

Now that we have found the value of x, we can find the total number of students in the school. We can represent the total number of students as the sum of the number of boys and girls:

Total number of students = 2x + 3x = 5x = 5(20) = 100

Therefore, the total number of students in the school is 100.

Conclusion

In this problem, we used algebra to solve a ratio and percentage problem. We represented the number of boys and girls in terms of x and used an equation to find the value of x. We then used the value of x to find the total number of students in the school.

Answer

The correct answer is 100.

Discussion

This problem requires the student to understand the concept of ratio and percentage and how to use algebra to solve problems involving these concepts. The student should be able to represent the number of boys and girls in terms of x and use an equation to find the value of x. The student should also be able to use the value of x to find the total number of students in the school.

Tips and Tricks

Make sure to read the problem carefully and understand what is being asked.
Represent the number of boys and girls in terms of x.
Use an equation to find the value of x.
Use the value of x to find the total number of students in the school.

Practice Questions

The ratio of number of boys to girls in a school is 3:5. If 20% of the boys is 4 more than 20% of the girls, then find the total number of students in the school.
The ratio of number of boys to girls in a school is 2:4. If 30% of the boys is 8 more than 30% of the girls, then find the total number of students in the school.

Solutions

Let's represent the number of boys as 3x and the number of girls as 5x. We can then use an equation to find the value of x:

0.2(3x) = 0.2(5x) + 4

Simplifying the equation, we get:

0.6x = 1x + 4

Subtracting 1x from both sides, we get:

-0.4x = 4

Dividing both sides by -0.4, we get:

x = -10

Since x cannot be negative, this solution is not valid.

Let's represent the number of boys as 2x and the number of girls as 4x. We can then use an equation to find the value of x:

0.3(2x) = 0.3(4x) + 8

Simplifying the equation, we get:

0.6x = 1.2x + 8

Subtracting 1.2x from both sides, we get:

-0.6x = 8

Dividing both sides by -0.6, we get:

x = -13.33

Since x cannot be negative, this solution is not valid.

Conclusion

In this article, we solved a ratio and percentage problem using algebra. We represented the number of boys and girls in terms of x and used an equation to find the value of x. We then used the value of x to find the total number of students in the school. We also provided tips and tricks for solving similar problems and practice questions for further practice.
COMPETITIVE MODULE CLASS VIII 13. ARITHMETIC REASONING WORKSHEET - 1 Q&A

Frequently Asked Questions and Answers

Q1: What is the ratio of boys to girls in the school?

A1: The ratio of boys to girls in the school is 2:3.

Q2: What is the percentage of girls that is 6 more than the 30% of boys?

A2: 30% of the girls is 6 more than 30% of the boys.

Q3: How can we represent the number of boys and girls in terms of x?

A3: We can represent the number of boys as 2x and the number of girls as 3x, where x is a constant.

Q4: What is the equation that we can use to find the value of x?

A4: The equation that we can use to find the value of x is:

0.3(3x) = 0.3(2x) + 6

Q5: How can we simplify the equation to find the value of x?

A5: We can simplify the equation by subtracting 0.6x from both sides, which gives us:

0.3x = 6

Q6: How can we find the value of x?

A6: We can find the value of x by dividing both sides of the equation by 0.3, which gives us:

x = 20

Q7: How can we find the total number of students in the school?

A7: We can find the total number of students in the school by adding the number of boys and girls, which gives us:

Total number of students = 2x + 3x = 5x = 5(20) = 100

Q8: What is the correct answer to the problem?

A8: The correct answer to the problem is 100.

Q9: What are some tips and tricks for solving similar problems?

A9: Some tips and tricks for solving similar problems include:

Make sure to read the problem carefully and understand what is being asked.
Represent the number of boys and girls in terms of x.
Use an equation to find the value of x.
Use the value of x to find the total number of students in the school.

Q10: What are some practice questions that we can use to further practice solving similar problems?

A10: Some practice questions that we can use to further practice solving similar problems include:

The ratio of number of boys to girls in a school is 3:5. If 20% of the boys is 4 more than 20% of the girls, then find the total number of students in the school.
The ratio of number of boys to girls in a school is 2:4. If 30% of the boys is 8 more than 30% of the girls, then find the total number of students in the school.

Q11: How can we solve the first practice question?

A11: To solve the first practice question, we can represent the number of boys as 3x and the number of girls as 5x. We can then use an equation to find the value of x:

0.2(3x) = 0.2(5x) + 4

Simplifying the equation, we get:

0.6x = 1x + 4

Subtracting 1x from both sides, we get:

-0.4x = 4

Dividing both sides by -0.4, we get:

x = -10

Since x cannot be negative, this solution is not valid.

Q12: How can we solve the second practice question?

A12: To solve the second practice question, we can represent the number of boys as 2x and the number of girls as 4x. We can then use an equation to find the value of x:

0.3(2x) = 0.3(4x) + 8

Simplifying the equation, we get:

0.6x = 1.2x + 8

Subtracting 1.2x from both sides, we get:

-0.6x = 8

Dividing both sides by -0.6, we get:

x = -13.33

Since x cannot be negative, this solution is not valid.

Conclusion

In this article, we provided a Q&A section for the competitive module class VIII 13. arithmetic reasoning worksheet - 1. We answered frequently asked questions and provided step-by-step solutions to practice questions. We also provided tips and tricks for solving similar problems.