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11. Three fourths of a number is equal to 60% of another number and the difference of these two numbers is 20. What is the sum of these two numbers?
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11. Three fourths of a number is equal to 60% of another number and th...
Understanding the Problem
To solve this problem, we need to define two variables for the two numbers. Let's denote:
- x = the first number
- y = the second number
Setting Up Equations
From the information provided, we can derive two equations:
1. Three-fourths of the first number equals 60% of the second number:
- (3/4)x = (60/100)y
- This simplifies to 3x = 2.4y (Multiplying both sides by 4)
2. The difference between the two numbers is 20:
- x - y = 20
Solving the Equations
Now, we can solve these equations step by step.
- Rearranging the second equation gives us:
- x = y + 20
- Substitute x in the first equation:
- 3(y + 20) = 2.4y
- 3y + 60 = 2.4y
- 3y - 2.4y = -60
- 0.6y = -60
- y = 100
- Now substituting y back into the equation for x:
- x = 100 + 20
- x = 120
Calculating the Sum
Finally, we need to find the sum of the two numbers:
- Sum = x + y = 120 + 100 = 220
Conclusion
The sum of the two numbers is 220.
To solve this problem, we need to define two variables for the two numbers. Let's denote:
- x = the first number
- y = the second number
Setting Up Equations
From the information provided, we can derive two equations:
1. Three-fourths of the first number equals 60% of the second number:
- (3/4)x = (60/100)y
- This simplifies to 3x = 2.4y (Multiplying both sides by 4)
2. The difference between the two numbers is 20:
- x - y = 20
Solving the Equations
Now, we can solve these equations step by step.
- Rearranging the second equation gives us:
- x = y + 20
- Substitute x in the first equation:
- 3(y + 20) = 2.4y
- 3y + 60 = 2.4y
- 3y - 2.4y = -60
- 0.6y = -60
- y = 100
- Now substituting y back into the equation for x:
- x = 100 + 20
- x = 120
Calculating the Sum
Finally, we need to find the sum of the two numbers:
- Sum = x + y = 120 + 100 = 220
Conclusion
The sum of the two numbers is 220.
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11. Three fourths of a number is equal to 60% of another number and the difference of these two numbers is 20. What is the sum of these two numbers?
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11. Three fourths of a number is equal to 60% of another number and the difference of these two numbers is 20. What is the sum of these two numbers? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 11. Three fourths of a number is equal to 60% of another number and the difference of these two numbers is 20. What is the sum of these two numbers? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 11. Three fourths of a number is equal to 60% of another number and the difference of these two numbers is 20. What is the sum of these two numbers?.
11. Three fourths of a number is equal to 60% of another number and the difference of these two numbers is 20. What is the sum of these two numbers? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 11. Three fourths of a number is equal to 60% of another number and the difference of these two numbers is 20. What is the sum of these two numbers? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 11. Three fourths of a number is equal to 60% of another number and the difference of these two numbers is 20. What is the sum of these two numbers?.
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