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If 3 is added to both the numerator and the denominator of a fraction, it becomes 5/7. If 6 is subtracted from both the numerator and the denominator, it becomes 1/2. What is the fraction?
- a)15/21
- b)12/18
- c)18/32
- d)10/17
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If 3 is added to both the numerator and the denominator of a fraction...
Let the fraction be x/y.
According to the question
(x + 3)/(y + 3) = 5/7 .... (i) and
(x - 6)/(y - 6) = 1/2 ..... (ii)
From equation (i) we get
7x + 21 = 5y + 15
7x - 5y = - 6 .... (iii)
From equation (ii) we get
2x - 12 = y - 6
2x - y = 6
10x - 5y = 30 .... (iv)
Subtracting (iii) from (iv) we get
3x = 36
x = 12
Use x = 12 in equation (iv) we get
y = 18
Hence, fraction = x/y = 12/18
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Community Answer
If 3 is added to both the numerator and the denominator of a fraction...
Given Information:
- After adding 3 to both the numerator and the denominator, the fraction becomes 5/7.
- After subtracting 6 from both the numerator and the denominator, the fraction becomes 1/2.
Let's assume the fraction to be x/y.
Step 1: Formulating the equations:
- Adding 3 to both the numerator and the denominator:
(x + 3) / (y + 3) = 5/7 ----(1)
- Subtracting 6 from both the numerator and the denominator:
(x - 6) / (y - 6) = 1/2 ----(2)
Step 2: Solving the equations:
Solving equation (1):
Cross multiplying, we get:
7(x + 3) = 5(y + 3)
7x + 21 = 5y + 15
7x - 5y = 15 - 21
7x - 5y = -6 ----(3)
Solving equation (2):
Cross multiplying, we get:
2(x - 6) = y - 6
2x - 12 = y - 6
2x - y = -6 + 12
2x - y = 6 ----(4)
Step 3: Solving the simultaneous equations:
Multiplying equation (4) by 5 and equation (3) by 2, we get:
10x - 5y = 30 ----(5)
14x - 10y = -12 ----(6)
Multiplying equation (5) by 2 and equation (6) by 5, we get:
20x - 10y = 60 ----(7)
70x - 50y = -60 ----(8)
Subtracting equation (7) from equation (8), we get:
50x = -120
x = -120/50
x = -12/5
Substituting the value of x in equation (4), we get:
2(-12/5) - y = 6
-24/5 - y = 6
-24 - 5y = 30
-5y = 30 + 24
-5y = 54
y = 54/(-5)
y = -54/5
Therefore, the fraction is -12/5 divided by -54/5, which simplifies to 12/18.
Hence, the correct answer is option B) 12/18.
- After adding 3 to both the numerator and the denominator, the fraction becomes 5/7.
- After subtracting 6 from both the numerator and the denominator, the fraction becomes 1/2.
Let's assume the fraction to be x/y.
Step 1: Formulating the equations:
- Adding 3 to both the numerator and the denominator:
(x + 3) / (y + 3) = 5/7 ----(1)
- Subtracting 6 from both the numerator and the denominator:
(x - 6) / (y - 6) = 1/2 ----(2)
Step 2: Solving the equations:
Solving equation (1):
Cross multiplying, we get:
7(x + 3) = 5(y + 3)
7x + 21 = 5y + 15
7x - 5y = 15 - 21
7x - 5y = -6 ----(3)
Solving equation (2):
Cross multiplying, we get:
2(x - 6) = y - 6
2x - 12 = y - 6
2x - y = -6 + 12
2x - y = 6 ----(4)
Step 3: Solving the simultaneous equations:
Multiplying equation (4) by 5 and equation (3) by 2, we get:
10x - 5y = 30 ----(5)
14x - 10y = -12 ----(6)
Multiplying equation (5) by 2 and equation (6) by 5, we get:
20x - 10y = 60 ----(7)
70x - 50y = -60 ----(8)
Subtracting equation (7) from equation (8), we get:
50x = -120
x = -120/50
x = -12/5
Substituting the value of x in equation (4), we get:
2(-12/5) - y = 6
-24/5 - y = 6
-24 - 5y = 30
-5y = 30 + 24
-5y = 54
y = 54/(-5)
y = -54/5
Therefore, the fraction is -12/5 divided by -54/5, which simplifies to 12/18.
Hence, the correct answer is option B) 12/18.
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If 3 is added to both the numerator and the denominator of a fraction, it becomes 5/7. If 6 is subtracted from both the numerator and the denominator, it becomes 1/2. What is the fraction?a)15/21b)12/18c)18/32d)10/17Correct answer is option 'B'. Can you explain this answer?
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