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The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to the denominator, the new number becomes 1/5. Then the original number was _______.
- a)7/11
- b)3/5
- c)5/8
- d)4/7
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The denominator of a rational number is greater than its numerator by ...
To solve this problem, let's first assign variables to the numerator and the denominator of the original rational number.
Let the numerator be x.
Then, the denominator is x + 3, as stated in the problem.
According to the given information, if 3 is subtracted from the numerator and 2 is added to the denominator, the new number becomes 1/5.
So, the new numerator is x - 3 and the new denominator is x + 3 + 2 = x + 5.
We can write this as an equation:
(x - 3)/(x + 5) = 1/5
To solve this equation, we can cross-multiply:
5(x - 3) = (x + 5)
Simplifying the equation:
5x - 15 = x + 5
Subtracting x from both sides:
4x - 15 = 5
Adding 15 to both sides:
4x = 20
Dividing both sides by 4:
x = 5
So, the numerator of the original rational number is 5.
Substituting this value back into the equation for the denominator:
x + 3 = 5 + 3 = 8
Therefore, the denominator of the original rational number is 8.
Hence, the original number is 5/8.
Therefore, the correct answer is option C) 5/8.
Let the numerator be x.
Then, the denominator is x + 3, as stated in the problem.
According to the given information, if 3 is subtracted from the numerator and 2 is added to the denominator, the new number becomes 1/5.
So, the new numerator is x - 3 and the new denominator is x + 3 + 2 = x + 5.
We can write this as an equation:
(x - 3)/(x + 5) = 1/5
To solve this equation, we can cross-multiply:
5(x - 3) = (x + 5)
Simplifying the equation:
5x - 15 = x + 5
Subtracting x from both sides:
4x - 15 = 5
Adding 15 to both sides:
4x = 20
Dividing both sides by 4:
x = 5
So, the numerator of the original rational number is 5.
Substituting this value back into the equation for the denominator:
x + 3 = 5 + 3 = 8
Therefore, the denominator of the original rational number is 8.
Hence, the original number is 5/8.
Therefore, the correct answer is option C) 5/8.
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Community Answer
The denominator of a rational number is greater than its numerator by ...
Let the number be x/y
According to the question,
y = x + 3 ⇒ x = y − 3 ... (1)
Also,
⇒ 5x – 15 = y + 2
⇒ 5x = y + 17 ...(2)
Solving (1) and (2), we get x = 5 and y = 8
∴ Required number = x/y = 5/8.
According to the question,
y = x + 3 ⇒ x = y − 3 ... (1)
Also,
⇒ 5x – 15 = y + 2⇒ 5x = y + 17 ...(2)
Solving (1) and (2), we get x = 5 and y = 8
∴ Required number = x/y = 5/8.
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The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to the denominator, the new number becomes 1/5.Then the original number was _______.a)7/11b)3/5c)5/8d)4/7Correct answer is option 'C'. Can you explain this answer?
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The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to the denominator, the new number becomes 1/5.Then the original number was _______.a)7/11b)3/5c)5/8d)4/7Correct answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to the denominator, the new number becomes 1/5.Then the original number was _______.a)7/11b)3/5c)5/8d)4/7Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to the denominator, the new number becomes 1/5.Then the original number was _______.a)7/11b)3/5c)5/8d)4/7Correct answer is option 'C'. Can you explain this answer?.
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