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Three fourths of one number is equal to 60% of another number and the difference between these two numbers is 20. What is the sum of these two numbers?
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Three fourths of one number is equal to 60% of another number and the ...
Understanding the Problem
To solve the problem, we need to define two variables based on the information provided:
- Let the first number be x.
- Let the second number be y.
Establishing Equations
From the problem, we can derive two equations:
1. Three fourths of the first number is equal to 60% of the second number:
- (3/4)x = (60/100)y
- Simplifying this gives us: 3x = 2.4y
2. The difference between these two numbers is 20:
- x - y = 20
Solving the Equations
Now, we have a system of two equations:
- 3x = 2.4y (Equation 1)
- x - y = 20 (Equation 2)
We can express y in terms of x from Equation 2:
- y = x - 20
Now, substitute y in Equation 1:
- 3x = 2.4(x - 20)
- 3x = 2.4x - 48
Now, isolate x:
- 3x - 2.4x = -48
- 0.6x = -48
- x = -48 / 0.6
- x = 80
Now, substitute x back to find y:
- y = 80 - 20
- y = 60
Final Calculation: Sum of the Numbers
Now that we have both numbers:
- x = 80
- y = 60
The sum of the two numbers is:
- Sum = x + y = 80 + 60 = 140
Conclusion
The sum of the two numbers is 140.
To solve the problem, we need to define two variables based on the information provided:
- Let the first number be x.
- Let the second number be y.
Establishing Equations
From the problem, we can derive two equations:
1. Three fourths of the first number is equal to 60% of the second number:
- (3/4)x = (60/100)y
- Simplifying this gives us: 3x = 2.4y
2. The difference between these two numbers is 20:
- x - y = 20
Solving the Equations
Now, we have a system of two equations:
- 3x = 2.4y (Equation 1)
- x - y = 20 (Equation 2)
We can express y in terms of x from Equation 2:
- y = x - 20
Now, substitute y in Equation 1:
- 3x = 2.4(x - 20)
- 3x = 2.4x - 48
Now, isolate x:
- 3x - 2.4x = -48
- 0.6x = -48
- x = -48 / 0.6
- x = 80
Now, substitute x back to find y:
- y = 80 - 20
- y = 60
Final Calculation: Sum of the Numbers
Now that we have both numbers:
- x = 80
- y = 60
The sum of the two numbers is:
- Sum = x + y = 80 + 60 = 140
Conclusion
The sum of the two numbers is 140.
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Three fourths of one number is equal to 60% of another number and the difference between these two numbers is 20. What is the sum of these two numbers?
Question Description
Three fourths of one number is equal to 60% of another number and the difference between these two numbers is 20. What is the sum of these two numbers? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Three fourths of one number is equal to 60% of another number and the difference between these two numbers is 20. What is the sum of these two numbers? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three fourths of one number is equal to 60% of another number and the difference between these two numbers is 20. What is the sum of these two numbers?.
Three fourths of one number is equal to 60% of another number and the difference between these two numbers is 20. What is the sum of these two numbers? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Three fourths of one number is equal to 60% of another number and the difference between these two numbers is 20. What is the sum of these two numbers? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three fourths of one number is equal to 60% of another number and the difference between these two numbers is 20. What is the sum of these two numbers?.
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