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If in a rational number denominator is greater than numerator by 8 if you increase the numerator by 17 and decrease the denominator by one you get 3 by 2 as result find the number?
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If in a rational number denominator is greater than numerator by 8 if ...
Understanding the Problem
To find the rational number, let's define the numerator as "x" and the denominator as "y". According to the problem:
- The denominator is greater than the numerator by 8:
y = x + 8
- When we increase the numerator by 17 and decrease the denominator by 1, the result is 3/2:
(x + 17) / (y - 1) = 3/2
Substituting the Values
Now, we can substitute the value of "y" from the first equation into the second equation.
- Replace y in the second equation:
(x + 17) / ((x + 8) - 1) = 3/2
Simplifying gives:
(x + 17) / (x + 7) = 3/2
Cross Multiplying
Cross-multiply to eliminate the fraction:
- 2(x + 17) = 3(x + 7)
Expanding both sides leads to:
- 2x + 34 = 3x + 21
Solving for x
Now, isolate x:
- 34 - 21 = 3x - 2x
- 13 = x
Thus, the numerator x = 13.
Finding the Denominator
Now, substitute x back into the equation for y:
- y = x + 8
- y = 13 + 8 = 21
Conclusion
The rational number is:
- Numerator: 13
- Denominator: 21
Thus, the rational number is 13/21.
To find the rational number, let's define the numerator as "x" and the denominator as "y". According to the problem:
- The denominator is greater than the numerator by 8:
y = x + 8
- When we increase the numerator by 17 and decrease the denominator by 1, the result is 3/2:
(x + 17) / (y - 1) = 3/2
Substituting the Values
Now, we can substitute the value of "y" from the first equation into the second equation.
- Replace y in the second equation:
(x + 17) / ((x + 8) - 1) = 3/2
Simplifying gives:
(x + 17) / (x + 7) = 3/2
Cross Multiplying
Cross-multiply to eliminate the fraction:
- 2(x + 17) = 3(x + 7)
Expanding both sides leads to:
- 2x + 34 = 3x + 21
Solving for x
Now, isolate x:
- 34 - 21 = 3x - 2x
- 13 = x
Thus, the numerator x = 13.
Finding the Denominator
Now, substitute x back into the equation for y:
- y = x + 8
- y = 13 + 8 = 21
Conclusion
The rational number is:
- Numerator: 13
- Denominator: 21
Thus, the rational number is 13/21.
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If in a rational number denominator is greater than numerator by 8 if you increase the numerator by 17 and decrease the denominator by one you get 3 by 2 as result find the number?
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If in a rational number denominator is greater than numerator by 8 if you increase the numerator by 17 and decrease the denominator by one you get 3 by 2 as result find the number? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If in a rational number denominator is greater than numerator by 8 if you increase the numerator by 17 and decrease the denominator by one you get 3 by 2 as result find the number? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If in a rational number denominator is greater than numerator by 8 if you increase the numerator by 17 and decrease the denominator by one you get 3 by 2 as result find the number?.
If in a rational number denominator is greater than numerator by 8 if you increase the numerator by 17 and decrease the denominator by one you get 3 by 2 as result find the number? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If in a rational number denominator is greater than numerator by 8 if you increase the numerator by 17 and decrease the denominator by one you get 3 by 2 as result find the number? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If in a rational number denominator is greater than numerator by 8 if you increase the numerator by 17 and decrease the denominator by one you get 3 by 2 as result find the number?.
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