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If the numerator of a fraction is increased by 1,it becomes 1/3and if the denominator is increased by 1,the fraction becomes 1.What is the fraction?
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If the numerator of a fraction is increased by 1,it becomes 1/3and if ...
Solution:
Given Information:
- Let the fraction be represented as x/y.
- When the numerator is increased by 1, the fraction becomes (x+1)/y = 1/3.
- When the denominator is increased by 1, the fraction becomes x/(y+1) = 1.
Finding the Fraction:
1. From the first condition, (x+1)/y = 1/3
- Cross multiply to get 3(x+1) = y
- Expand the equation to get 3x + 3 = y
2. From the second condition, x/(y+1) = 1
- Cross multiply to get x = y + 1
3. Substitute the value of x from the second condition into the first condition:
- 3(y+1) + 3 = y
- Simplify the equation to get 3y + 3 + 3 = y
- Further simplify to get 3y + 6 = y
- Solve for y to get y = 6
4. Substitute the value of y into the second condition to find x:
- x = 6 + 1
- x = 7
5. Therefore, the fraction is 7/6.
Conclusion:
The fraction is 7/6, where the numerator is 7 and the denominator is 6.
Given Information:
- Let the fraction be represented as x/y.
- When the numerator is increased by 1, the fraction becomes (x+1)/y = 1/3.
- When the denominator is increased by 1, the fraction becomes x/(y+1) = 1.
Finding the Fraction:
1. From the first condition, (x+1)/y = 1/3
- Cross multiply to get 3(x+1) = y
- Expand the equation to get 3x + 3 = y
2. From the second condition, x/(y+1) = 1
- Cross multiply to get x = y + 1
3. Substitute the value of x from the second condition into the first condition:
- 3(y+1) + 3 = y
- Simplify the equation to get 3y + 3 + 3 = y
- Further simplify to get 3y + 6 = y
- Solve for y to get y = 6
4. Substitute the value of y into the second condition to find x:
- x = 6 + 1
- x = 7
5. Therefore, the fraction is 7/6.
Conclusion:
The fraction is 7/6, where the numerator is 7 and the denominator is 6.
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If the numerator of a fraction is increased by 1,it becomes 1/3and if the denominator is increased by 1,the fraction becomes 1.What is the fraction?
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If the numerator of a fraction is increased by 1,it becomes 1/3and if the denominator is increased by 1,the fraction becomes 1.What is the fraction? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the numerator of a fraction is increased by 1,it becomes 1/3and if the denominator is increased by 1,the fraction becomes 1.What is the fraction? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the numerator of a fraction is increased by 1,it becomes 1/3and if the denominator is increased by 1,the fraction becomes 1.What is the fraction?.
If the numerator of a fraction is increased by 1,it becomes 1/3and if the denominator is increased by 1,the fraction becomes 1.What is the fraction? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the numerator of a fraction is increased by 1,it becomes 1/3and if the denominator is increased by 1,the fraction becomes 1.What is the fraction? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the numerator of a fraction is increased by 1,it becomes 1/3and if the denominator is increased by 1,the fraction becomes 1.What is the fraction?.
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