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Fourth-fifth of a number is 10 more than two- thirds of the number .find the number?
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Fourth-fifth of a number is 10 more than two- thirds of the number .fi...
Problem Statement
We need to find a number where four-fifths of it is 10 more than two-thirds of it.
Let the Number Be x
- We denote the unknown number as "x".
Formulating the Equation
- According to the problem, we can express the relationship as:
- (4/5)x = (2/3)x + 10
Clearing Fractions
- To eliminate the fractions, we can multiply the entire equation by a common multiple of the denominators (15 in this case):
- 15 * (4/5)x = 15 * (2/3)x + 15 * 10
- This simplifies to:
- 12x = 10x + 150
Simplifying the Equation
- Now, we rearrange the equation:
- 12x - 10x = 150
- 2x = 150
Finding the Value of x
- Dividing both sides by 2:
- x = 75
Conclusion
- The number we are looking for is 75.
Verification
- To verify, calculate:
- Four-fifths of 75: (4/5) * 75 = 60
- Two-thirds of 75: (2/3) * 75 = 50
- Check if 60 is indeed 10 more than 50: 50 + 10 = 60
- This confirms our solution is correct.
Therefore, the number is 75.
We need to find a number where four-fifths of it is 10 more than two-thirds of it.
Let the Number Be x
- We denote the unknown number as "x".
Formulating the Equation
- According to the problem, we can express the relationship as:
- (4/5)x = (2/3)x + 10
Clearing Fractions
- To eliminate the fractions, we can multiply the entire equation by a common multiple of the denominators (15 in this case):
- 15 * (4/5)x = 15 * (2/3)x + 15 * 10
- This simplifies to:
- 12x = 10x + 150
Simplifying the Equation
- Now, we rearrange the equation:
- 12x - 10x = 150
- 2x = 150
Finding the Value of x
- Dividing both sides by 2:
- x = 75
Conclusion
- The number we are looking for is 75.
Verification
- To verify, calculate:
- Four-fifths of 75: (4/5) * 75 = 60
- Two-thirds of 75: (2/3) * 75 = 50
- Check if 60 is indeed 10 more than 50: 50 + 10 = 60
- This confirms our solution is correct.
Therefore, the number is 75.
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Fourth-fifth of a number is 10 more than two- thirds of the number .find the number?
Question Description
Fourth-fifth of a number is 10 more than two- thirds of the number .find the number? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Fourth-fifth of a number is 10 more than two- thirds of the number .find the number? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Fourth-fifth of a number is 10 more than two- thirds of the number .find the number?.
Fourth-fifth of a number is 10 more than two- thirds of the number .find the number? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Fourth-fifth of a number is 10 more than two- thirds of the number .find the number? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Fourth-fifth of a number is 10 more than two- thirds of the number .find the number?.
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