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The difference of two numbers is 72 and the questions obtained by dividing the one by other is 3 find the numbers?
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The difference of two numbers is 72 and the questions obtained by divi...
Certainly! Let’s solve the problem step by step.
Given Information
- The difference of two numbers is 72.
- The ratio of the two numbers is 3.
Let’s Define the Variables
- Let the two numbers be \( x \) and \( y \).
- According to the problem, we have:
- \( x - y = 72 \) (1)
- \( \frac{x}{y} = 3 \) (2)
Expressing One Variable in Terms of Another
From equation (2), we can express \( x \) in terms of \( y \):
- \( x = 3y \) (3)
Substituting into the Difference Equation
Now, substitute equation (3) into equation (1):
- \( 3y - y = 72 \)
This simplifies to:
- \( 2y = 72 \)
Solving for \( y \)
To find \( y \):
- \( y = \frac{72}{2} = 36 \)
Finding \( x \)
Using equation (3) to find \( x \):
- \( x = 3y = 3 \times 36 = 108 \)
Conclusion
Thus, the two numbers are:
- \( x = 108 \)
- \( y = 36 \)
Final Verification
- Difference: \( 108 - 36 = 72 \)
- Ratio: \( \frac{108}{36} = 3 \)
Both conditions are satisfied. The two numbers are 108 and 36.
Given Information
- The difference of two numbers is 72.
- The ratio of the two numbers is 3.
Let’s Define the Variables
- Let the two numbers be \( x \) and \( y \).
- According to the problem, we have:
- \( x - y = 72 \) (1)
- \( \frac{x}{y} = 3 \) (2)
Expressing One Variable in Terms of Another
From equation (2), we can express \( x \) in terms of \( y \):
- \( x = 3y \) (3)
Substituting into the Difference Equation
Now, substitute equation (3) into equation (1):
- \( 3y - y = 72 \)
This simplifies to:
- \( 2y = 72 \)
Solving for \( y \)
To find \( y \):
- \( y = \frac{72}{2} = 36 \)
Finding \( x \)
Using equation (3) to find \( x \):
- \( x = 3y = 3 \times 36 = 108 \)
Conclusion
Thus, the two numbers are:
- \( x = 108 \)
- \( y = 36 \)
Final Verification
- Difference: \( 108 - 36 = 72 \)
- Ratio: \( \frac{108}{36} = 3 \)
Both conditions are satisfied. The two numbers are 108 and 36.
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The difference of two numbers is 72 and the questions obtained by dividing the one by other is 3 find the numbers?
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The difference of two numbers is 72 and the questions obtained by dividing the one by other is 3 find the numbers? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The difference of two numbers is 72 and the questions obtained by dividing the one by other is 3 find the numbers? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference of two numbers is 72 and the questions obtained by dividing the one by other is 3 find the numbers?.
The difference of two numbers is 72 and the questions obtained by dividing the one by other is 3 find the numbers? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The difference of two numbers is 72 and the questions obtained by dividing the one by other is 3 find the numbers? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference of two numbers is 72 and the questions obtained by dividing the one by other is 3 find the numbers?.
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