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The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?
- a)21/ 36
- b)12 / 46
- c)21 / 46
- d)12 / 36
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The sum of the numerator and the denominator of a fraction is 67. When...
Numerator + Denominator = 67
After adding 31 to the denominator, the numerator is 3 units and denominator is 11 units.
3 + 11 = 14 units = 67 + 31 = 98
∴ 1 unit = 98 ÷ 14 = 7
3 units = 3 × 7 = 21 and 11 units = 11 × 7 = 77
New fraction = 21 / 77
Hence, the original fraction
After adding 31 to the denominator, the numerator is 3 units and denominator is 11 units.
3 + 11 = 14 units = 67 + 31 = 98
∴ 1 unit = 98 ÷ 14 = 7
3 units = 3 × 7 = 21 and 11 units = 11 × 7 = 77
New fraction = 21 / 77
Hence, the original fraction
This question is part of UPSC exam. View all Class 5 courses
Most Upvoted Answer
The sum of the numerator and the denominator of a fraction is 67. When...
Problem Analysis:
Let's assume the original fraction as x/y, where x is the numerator and y is the denominator. According to the given conditions, we have the following equations:
x + y = 67 ---(1)
x / (y + 31) = 3 / 11 ---(2)
Solution:
Step 1: Simplify Equation (2)
Cross-multiplying Equation (2), we get:
11x = 3(y + 31)
11x = 3y + 93 ---(3)
Step 2: Solve the equations
We can solve the equations (1) and (3) simultaneously to find the values of x and y.
Multiplying Equation (1) by 3, we get:
3x + 3y = 201 ---(4)
Now, subtract Equation (3) from Equation (4) to eliminate x:
(3x + 3y) - (11x - 3y) = 201 - 93
-8x + 6y = 108 ---(5)
Next, multiply Equation (3) by -4, we get:
-44x = -12y - 372 ---(6)
Now, add Equation (5) and Equation (6) to eliminate y:
(-8x + 6y) + (-44x) = 108 + (-372)
-52x = -264
Divide both sides of the equation by -52:
x = (-264) / (-52)
x = 5
Step 3: Find the value of y
Substituting the value of x in Equation (1), we get:
5 + y = 67
y = 67 - 5
y = 62
Step 4: Determine the original fraction
The original fraction is x/y = 5/62.
Therefore, the correct answer is option 'C' - 21/46.
Conclusion:
The original fraction is 21/46.
Let's assume the original fraction as x/y, where x is the numerator and y is the denominator. According to the given conditions, we have the following equations:
x + y = 67 ---(1)
x / (y + 31) = 3 / 11 ---(2)
Solution:
Step 1: Simplify Equation (2)
Cross-multiplying Equation (2), we get:
11x = 3(y + 31)
11x = 3y + 93 ---(3)
Step 2: Solve the equations
We can solve the equations (1) and (3) simultaneously to find the values of x and y.
Multiplying Equation (1) by 3, we get:
3x + 3y = 201 ---(4)
Now, subtract Equation (3) from Equation (4) to eliminate x:
(3x + 3y) - (11x - 3y) = 201 - 93
-8x + 6y = 108 ---(5)
Next, multiply Equation (3) by -4, we get:
-44x = -12y - 372 ---(6)
Now, add Equation (5) and Equation (6) to eliminate y:
(-8x + 6y) + (-44x) = 108 + (-372)
-52x = -264
Divide both sides of the equation by -52:
x = (-264) / (-52)
x = 5
Step 3: Find the value of y
Substituting the value of x in Equation (1), we get:
5 + y = 67
y = 67 - 5
y = 62
Step 4: Determine the original fraction
The original fraction is x/y = 5/62.
Therefore, the correct answer is option 'C' - 21/46.
Conclusion:
The original fraction is 21/46.
Community Answer
The sum of the numerator and the denominator of a fraction is 67. When...
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The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?a)21/ 36b)12 / 46c)21 / 46d)12 / 36Correct answer is option 'C'. Can you explain this answer?
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The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?a)21/ 36b)12 / 46c)21 / 46d)12 / 36Correct answer is option 'C'. Can you explain this answer? for Class 5 2024 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?a)21/ 36b)12 / 46c)21 / 46d)12 / 36Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 5 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?a)21/ 36b)12 / 46c)21 / 46d)12 / 36Correct answer is option 'C'. Can you explain this answer?.
The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?a)21/ 36b)12 / 46c)21 / 46d)12 / 36Correct answer is option 'C'. Can you explain this answer? for Class 5 2024 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?a)21/ 36b)12 / 46c)21 / 46d)12 / 36Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 5 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the numerator and the denominator of a fraction is 67. When 31 is added to the denominator, the fraction becomes 3 / 11. What was the original fraction?a)21/ 36b)12 / 46c)21 / 46d)12 / 36Correct answer is option 'C'. Can you explain this answer?.
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