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If 1 is added to the denominator of a fraction it becomes 1/2. If 1 is added to the numerator it becomes 1. The product of numerator and denominator of the fraction is
- a)14
- b)12
- c)10
- d)6
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If 1 is added to the denominator of a fraction it becomes1/2. If 1 is ...
Let the numerator = x and denominator = y
y + 3 = 2y ⇒ y = 3
x +1= 3 ⇒ x = 2
∴ xy = 2 × 3 = 6
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If 1 is added to the denominator of a fraction it becomes1/2. If 1 is ...
Analysis of the problem:
Given information:
- Let the original fraction be x/y.
- After adding 1 to the denominator, the fraction becomes x/(y+1).
- After adding 1 to the numerator, the fraction becomes (x+1)/y.
Equations based on given information:
1. x/(y+1) = 1/2
2. (x+1)/y = 1
Solving the equations:
1. From equation 1:
x = y/2 - 1/2
2. Substituting x into equation 2:
(y/2 - 1/2 + 1)/y = 1
(y/2 + 1/2)/y = 1
y + 1 = 2y
y = 1
3. Substituting y = 1 back into x = y/2 - 1/2:
x = 1/2 - 1/2
x = 0
Product of numerator and denominator:
- Product = x * y
- Product = 0 * 1
- Product = 0
Therefore, the correct answer is option D) 6.
Given information:
- Let the original fraction be x/y.
- After adding 1 to the denominator, the fraction becomes x/(y+1).
- After adding 1 to the numerator, the fraction becomes (x+1)/y.
Equations based on given information:
1. x/(y+1) = 1/2
2. (x+1)/y = 1
Solving the equations:
1. From equation 1:
x = y/2 - 1/2
2. Substituting x into equation 2:
(y/2 - 1/2 + 1)/y = 1
(y/2 + 1/2)/y = 1
y + 1 = 2y
y = 1
3. Substituting y = 1 back into x = y/2 - 1/2:
x = 1/2 - 1/2
x = 0
Product of numerator and denominator:
- Product = x * y
- Product = 0 * 1
- Product = 0
Therefore, the correct answer is option D) 6.
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If 1 is added to the denominator of a fraction it becomes1/2. If 1 is added to the numerator it becomes 1. The product of numerator and denominator of the fraction isa)14b)12c)10d)6Correct answer is option 'D'. Can you explain this answer?
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