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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 increased by 12.
- a)3/8
- b)5/8
- c)2/8
- d)2/3
Correct answer is option 'A'. Can you explain this answer?
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Find the fraction which is equal to 1/2 when both its numerator and de...
**Solution:**
Let's assume the fraction to be x/y. According to the given information, we have two equations:
1) (x+2)/(y+2) = 1/2 -- Equation 1
2) (x+12)/(y+12) = 3/4 -- Equation 2
We need to find the value of x/y.
To solve this problem, we will use the method of substitution.
**Step 1: Simplify Equation 1**
Multiplying both sides of Equation 1 by 2(y+2), we get:
2(x+2) = y+2
Expanding and simplifying,
2x + 4 = y + 2
2x = y - 2 -- Equation 3
**Step 2: Simplify Equation 2**
Multiplying both sides of Equation 2 by 4(y+12), we get:
4(x+12) = 3(y+12)
Expanding and simplifying,
4x + 48 = 3y + 36
4x = 3y - 12 -- Equation 4
**Step 3: Solve the equations**
Now, we have two equations:
2x = y - 2 -- Equation 3
4x = 3y - 12 -- Equation 4
We can substitute the value of y from Equation 3 into Equation 4:
4x = 3(2x + 2) - 12
Expanding and simplifying,
4x = 6x + 6 - 12
4x - 6x = -6
-2x = -6
x = 3
Substituting the value of x into Equation 3,
2(3) = y - 2
6 = y - 2
y = 8
Therefore, the fraction is 3/8.
Hence, option 'A' is the correct answer.
Let's assume the fraction to be x/y. According to the given information, we have two equations:
1) (x+2)/(y+2) = 1/2 -- Equation 1
2) (x+12)/(y+12) = 3/4 -- Equation 2
We need to find the value of x/y.
To solve this problem, we will use the method of substitution.
**Step 1: Simplify Equation 1**
Multiplying both sides of Equation 1 by 2(y+2), we get:
2(x+2) = y+2
Expanding and simplifying,
2x + 4 = y + 2
2x = y - 2 -- Equation 3
**Step 2: Simplify Equation 2**
Multiplying both sides of Equation 2 by 4(y+12), we get:
4(x+12) = 3(y+12)
Expanding and simplifying,
4x + 48 = 3y + 36
4x = 3y - 12 -- Equation 4
**Step 3: Solve the equations**
Now, we have two equations:
2x = y - 2 -- Equation 3
4x = 3y - 12 -- Equation 4
We can substitute the value of y from Equation 3 into Equation 4:
4x = 3(2x + 2) - 12
Expanding and simplifying,
4x = 6x + 6 - 12
4x - 6x = -6
-2x = -6
x = 3
Substituting the value of x into Equation 3,
2(3) = y - 2
6 = y - 2
y = 8
Therefore, the fraction is 3/8.
Hence, option 'A' is the correct answer.
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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 increased by 12.a)3/8b)5/8c)2/8d)2/3Correct answer is option 'A'. Can you explain this answer?
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