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A fraction becomes 6/5 when 5 is added to its numerator and becomes 1/2 when 4 is added to its denominator. What will be the value of the fraction?
- a)8/9
- b)7/10
- c)7/8
- d)6/11
Correct answer is option 'B'. Can you explain this answer?
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A fraction becomes 6/5 when 5 is added to its numerator and becomes 1/...
To solve this problem, let's assume the fraction to be x/y.
Step 1: Write the given information as equations
We are given two pieces of information:
1) When 5 is added to the numerator, the fraction becomes 6/5. So we can write the equation as:
(x + 5)/y = 6/5
2) When 4 is added to the denominator, the fraction becomes 1/2. So we can write the equation as:
x/(y + 4) = 1/2
Step 2: Solve the equations simultaneously
To solve these equations, we can use the method of substitution.
From equation 1, we can rewrite it as:
x + 5 = (6/5)y
Now, solve equation 2 for x:
2x = y + 4
x = (y + 4)/2
Step 3: Substitute the value of x from equation 2 into equation 1
Substituting (y + 4)/2 for x in equation 1, we get:
[(y + 4)/2 + 5]/y = 6/5
Simplifying the equation:
[(y + 4 + 10)/2]/y = 6/5
(y + 14)/2y = 6/5
Cross multiply:
5(y + 14) = 6(2y)
5y + 70 = 12y
Rearranging the equation:
12y - 5y = 70
7y = 70
y = 10
Step 4: Find the value of x
Substituting the value of y = 10 into equation 2:
x = (10 + 4)/2
x = 14/2
x = 7
Therefore, the fraction is 7/10, which matches with option B.
Step 1: Write the given information as equations
We are given two pieces of information:
1) When 5 is added to the numerator, the fraction becomes 6/5. So we can write the equation as:
(x + 5)/y = 6/5
2) When 4 is added to the denominator, the fraction becomes 1/2. So we can write the equation as:
x/(y + 4) = 1/2
Step 2: Solve the equations simultaneously
To solve these equations, we can use the method of substitution.
From equation 1, we can rewrite it as:
x + 5 = (6/5)y
Now, solve equation 2 for x:
2x = y + 4
x = (y + 4)/2
Step 3: Substitute the value of x from equation 2 into equation 1
Substituting (y + 4)/2 for x in equation 1, we get:
[(y + 4)/2 + 5]/y = 6/5
Simplifying the equation:
[(y + 4 + 10)/2]/y = 6/5
(y + 14)/2y = 6/5
Cross multiply:
5(y + 14) = 6(2y)
5y + 70 = 12y
Rearranging the equation:
12y - 5y = 70
7y = 70
y = 10
Step 4: Find the value of x
Substituting the value of y = 10 into equation 2:
x = (10 + 4)/2
x = 14/2
x = 7
Therefore, the fraction is 7/10, which matches with option B.
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A fraction becomes 6/5 when 5 is added to its numerator and becomes 1/2 when 4 is added to its denominator. What will be the value of the fraction?a)8/9b)7/10c)7/8d)6/11Correct answer is option 'B'. Can you explain this answer?
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