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Find the fraction which is equal to 1/2 when both its numerator and denominator are increased by 2. It is equal to 3/4 when both are incresed by 12.
- a)3/8
- b)5/8
- c)2/3
- d)none
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Find the fraction which is equal to 1/2 when both its numerator and de...
Let the numerator be x and denomentar be y
(x+2)/(y+2)=1/2
2x+4=y+2
2x-y=-2
4x-2y=-4
when
(x+12)/(y+12)=3/4
4x+48=3y+36
4x-3y=-12
from both the eq
y=8
x=3
so fraction is
3/8
Most Upvoted Answer
Find the fraction which is equal to 1/2 when both its numerator and de...
Given Information:
- The fraction becomes 1/2 when both its numerator and denominator are increased by 2.
- The fraction becomes 3/4 when both its numerator and denominator are increased by 12.
To Find: The fraction
Solution:
Let's assume the fraction to be x/y.
According to the first condition,
- When both the numerator and denominator are increased by 2, the fraction becomes 1/2.
- Therefore, (x+2)/(y+2) = 1/2
Simplifying this equation, we get:
- 2(x+2) = y+2
- 2x + 4 = y + 2
- 2x = y - 2
According to the second condition,
- When both the numerator and denominator are increased by 12, the fraction becomes 3/4.
- Therefore, (x+12)/(y+12) = 3/4
Simplifying this equation, we get:
- 4(x+12) = 3(y+12)
- 4x + 48 = 3y + 36
- 4x = 3y - 12
Now we have two equations:
- 2x = y - 2
- 4x = 3y - 12
We can solve these two equations to find the values of x and y.
Multiplying the first equation by 2, we get:
- 4x = 2y - 4
Now we have two equations with the same value of 4x:
- 4x = 3y - 12
- 4x = 2y - 4
Equating both equations, we get:
- 3y - 12 = 2y - 4
- y = 8
Substituting the value of y in the first equation, we get:
- 2x = y - 2
- 2x = 8 - 2
- x = 3
Therefore, the fraction is 3/8.
Answer: Option A (3/8)
- The fraction becomes 1/2 when both its numerator and denominator are increased by 2.
- The fraction becomes 3/4 when both its numerator and denominator are increased by 12.
To Find: The fraction
Solution:
Let's assume the fraction to be x/y.
According to the first condition,
- When both the numerator and denominator are increased by 2, the fraction becomes 1/2.
- Therefore, (x+2)/(y+2) = 1/2
Simplifying this equation, we get:
- 2(x+2) = y+2
- 2x + 4 = y + 2
- 2x = y - 2
According to the second condition,
- When both the numerator and denominator are increased by 12, the fraction becomes 3/4.
- Therefore, (x+12)/(y+12) = 3/4
Simplifying this equation, we get:
- 4(x+12) = 3(y+12)
- 4x + 48 = 3y + 36
- 4x = 3y - 12
Now we have two equations:
- 2x = y - 2
- 4x = 3y - 12
We can solve these two equations to find the values of x and y.
Multiplying the first equation by 2, we get:
- 4x = 2y - 4
Now we have two equations with the same value of 4x:
- 4x = 3y - 12
- 4x = 2y - 4
Equating both equations, we get:
- 3y - 12 = 2y - 4
- y = 8
Substituting the value of y in the first equation, we get:
- 2x = y - 2
- 2x = 8 - 2
- x = 3
Therefore, the fraction is 3/8.
Answer: Option A (3/8)
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Community Answer
Find the fraction which is equal to 1/2 when both its numerator and de...
A - 3/8.. It's simple 3+2=5/8+2=10 Hence it is 1/2.
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