Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > RS Aggarwal Solutions: Exercise 8B - Linear Equations
RS Aggarwal Solutions: Exercise 8B - Linear Equations | Mathematics (Maths) Class 8 PDF Download
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Page 1
Question 1.
Two numbers are in the ratio 8:3. If the sum of the numbers is 143, find the numbers.
Answer:
Since the numbers are in the ratio 8:3 so Let the numbers be 8x and 3x
According to the question
Page 2
Question 1.
Two numbers are in the ratio 8:3. If the sum of the numbers is 143, find the numbers.
Answer:
Since the numbers are in the ratio 8:3 so Let the numbers be 8x and 3x
According to the question
8x + 3x = 143
? 11x = 143
? x = 13
So the numbers are 8x = 8 × 13 = 104 and 3x = 3 × 13 = 39
Question 2.
of a number is 20 less than the original number. Find the number.
Answer:
Let the numbers be x
According to the question
By cross multiplication
Taking LCM of 1 and 3 on LHS = 3
? x = 60
So the number 60
Question 3.
Four - fifths of a number is 10 more than two - thirds of the number. Find the number.
Answer:
Let the numbers be x
According to the question
Page 3
Question 1.
Two numbers are in the ratio 8:3. If the sum of the numbers is 143, find the numbers.
Answer:
Since the numbers are in the ratio 8:3 so Let the numbers be 8x and 3x
According to the question
8x + 3x = 143
? 11x = 143
? x = 13
So the numbers are 8x = 8 × 13 = 104 and 3x = 3 × 13 = 39
Question 2.
of a number is 20 less than the original number. Find the number.
Answer:
Let the numbers be x
According to the question
By cross multiplication
Taking LCM of 1 and 3 on LHS = 3
? x = 60
So the number 60
Question 3.
Four - fifths of a number is 10 more than two - thirds of the number. Find the number.
Answer:
Let the numbers be x
According to the question
? 2x = 10 × 15 = 150
? x = 75
So the number is 75.
Question 4.
Twenty - four is divided into two parts such that 7 times the first part added to 5 times the second part makes 146. Find
each part.
Answer:
Let the two parts be x and (24 - x)
According to the question
7x + 5(24 - x) = 146
By cross multiplication
? 2x = 146 - 120
? 2x = 26
? x = 13
So the parts are 13 and (24 - 13) = 11
Question 5.
Find the number whose fifth part increased by 5 is equal to its fourth part diminished by 5.
Answer:
Let the numbers be x
According to the question
Page 4
Question 1.
Two numbers are in the ratio 8:3. If the sum of the numbers is 143, find the numbers.
Answer:
Since the numbers are in the ratio 8:3 so Let the numbers be 8x and 3x
According to the question
8x + 3x = 143
? 11x = 143
? x = 13
So the numbers are 8x = 8 × 13 = 104 and 3x = 3 × 13 = 39
Question 2.
of a number is 20 less than the original number. Find the number.
Answer:
Let the numbers be x
According to the question
By cross multiplication
Taking LCM of 1 and 3 on LHS = 3
? x = 60
So the number 60
Question 3.
Four - fifths of a number is 10 more than two - thirds of the number. Find the number.
Answer:
Let the numbers be x
According to the question
? 2x = 10 × 15 = 150
? x = 75
So the number is 75.
Question 4.
Twenty - four is divided into two parts such that 7 times the first part added to 5 times the second part makes 146. Find
each part.
Answer:
Let the two parts be x and (24 - x)
According to the question
7x + 5(24 - x) = 146
By cross multiplication
? 2x = 146 - 120
? 2x = 26
? x = 13
So the parts are 13 and (24 - 13) = 11
Question 5.
Find the number whose fifth part increased by 5 is equal to its fourth part diminished by 5.
Answer:
Let the numbers be x
According to the question
Taking LCM of 5 and 1 on LHS = 5 and 4 and 1 on RHS = 1
?
So the number 200
Question 6.
Three numbers are in the ratio of 4 : 5 : 6. If the sum of the largest and the smallest equals the sum of the third and 55,
find the numbers.
Answer:
Let the numbers be 4x,5x and 6x
According to the question
6x + 4x = 5x + 55
By cross multiplication
? 10x - 5x = 55
? 5x = 55
? x = 11
So the numbers are 4x = 4 × 11 = 44, 5x = 5 × 11 = 55 and 6x = 6 × 11 = 66
Question 7.
If 10 be added to four times a certain number, the result is 5 less than five times the number. Find the number.
Answer:
Let the number be x
According to the question
Page 5
Question 1.
Two numbers are in the ratio 8:3. If the sum of the numbers is 143, find the numbers.
Answer:
Since the numbers are in the ratio 8:3 so Let the numbers be 8x and 3x
According to the question
8x + 3x = 143
? 11x = 143
? x = 13
So the numbers are 8x = 8 × 13 = 104 and 3x = 3 × 13 = 39
Question 2.
of a number is 20 less than the original number. Find the number.
Answer:
Let the numbers be x
According to the question
By cross multiplication
Taking LCM of 1 and 3 on LHS = 3
? x = 60
So the number 60
Question 3.
Four - fifths of a number is 10 more than two - thirds of the number. Find the number.
Answer:
Let the numbers be x
According to the question
? 2x = 10 × 15 = 150
? x = 75
So the number is 75.
Question 4.
Twenty - four is divided into two parts such that 7 times the first part added to 5 times the second part makes 146. Find
each part.
Answer:
Let the two parts be x and (24 - x)
According to the question
7x + 5(24 - x) = 146
By cross multiplication
? 2x = 146 - 120
? 2x = 26
? x = 13
So the parts are 13 and (24 - 13) = 11
Question 5.
Find the number whose fifth part increased by 5 is equal to its fourth part diminished by 5.
Answer:
Let the numbers be x
According to the question
Taking LCM of 5 and 1 on LHS = 5 and 4 and 1 on RHS = 1
?
So the number 200
Question 6.
Three numbers are in the ratio of 4 : 5 : 6. If the sum of the largest and the smallest equals the sum of the third and 55,
find the numbers.
Answer:
Let the numbers be 4x,5x and 6x
According to the question
6x + 4x = 5x + 55
By cross multiplication
? 10x - 5x = 55
? 5x = 55
? x = 11
So the numbers are 4x = 4 × 11 = 44, 5x = 5 × 11 = 55 and 6x = 6 × 11 = 66
Question 7.
If 10 be added to four times a certain number, the result is 5 less than five times the number. Find the number.
Answer:
Let the number be x
According to the question
10 + 4x = 5x - 5 [ 10 is added to 4 times the number, 5 less than 5 times the number]
By transposing
? 5x - 4x = 10 + 5
? x = 15
So the number is 15
Question 8.
Two numbers are such that the ratio between them is 3 : 5. If each is increased by 10, the ratio between the new
numbers so formed is 5:7. Find the original numbers.
Answer:
Let the numbers be 3x and 5x
According to the question
By cross multiplication
? 7(3x + 10) = 5(5x + 10)
? 21x + 70 = 25x + 50
? 4x = 20
? x = 5
So the numbers are 3x = 3 × 5 = 15 and 5x = 5 × 5 = 25
Question 9.
Find three consecutive odd numbers whose sum is 147. Hint. Let the required numbers be (2x + 1), (2x + 3) and (2x +
5).
Answer:
Let the numbers be (2x + 1), (2x + 3) and (2x + 5)
According to the question
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FAQs on RS Aggarwal Solutions: Exercise 8B - Linear Equations - Mathematics (Maths) Class 8
| 1. What are linear equations? |  |
Ans. Linear equations are equations with two variables that can be represented by a straight line on a graph. They are in the form of ax + by = c, where a, b, and c are constants and x and y are variables.
| 2. How do you solve a linear equation? | |
Ans. To solve a linear equation, you need to isolate the variable on one side of the equation. You can do this by performing operations such as addition, subtraction, multiplication, and division on both sides of the equation. The goal is to simplify the equation until you have the variable on one side and the constant on the other side.
| 3. What is the importance of solving linear equations? | |
Ans. Solving linear equations is important as it helps in finding the values of variables and understanding the relationship between them. It is a fundamental concept in algebra and is used in various real-life situations such as calculating distances, determining rates, and solving problems involving proportions.
| 4. How many solutions can a linear equation have? | |
Ans. A linear equation can have three types of solutions: one solution, no solution, or infinitely many solutions. If the equation represents two lines that intersect at one point, it has one solution. If the equation represents two parallel lines, it has no solution. And if the equation represents two coincident lines, it has infinitely many solutions.
| 5. Can linear equations be solved graphically? | |
Ans. Yes, linear equations can be solved graphically by plotting the equations on a coordinate plane and finding the point of intersection (if any) of the two lines. The coordinates of the point of intersection will give the solution to the linear equation system. Graphical solutions are particularly useful when dealing with simultaneous linear equations.
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Nov 30, 2024 Last updated |
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