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The sum of the numerator and denominator of a certain fraction is 8. If 2 is added to both the numerator and the denominator the value of the fraction increased by 4/35, then the fraction is:
- a)1/7
- b)3/5
- c)5/3
- d)Can not be determined
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The sum of the numerator and denominator of a certain fraction is 8. ...
Let fraction be x/y by given condition
x + y = 8 …………(i)
and x + 2 / y + 2 - x / y = 4 / 35
or 2x + 2y -xy -2x / y(y +2) = 4 / 35
or 2(y -x) / y(y +2) = 4 / 35
or 35 (y - x) = 2y (y + 2) …………(ii)
From (i)
x = 8 - y
substituting this value in (ii)
35 (y - 8 = y) - 2y(y + 2)
35 (y - 4) = y (y + 2)
y2 - 33y + 140 = 0
y = 28 or 5
We cannot take , taking y = 5 x will become 3
Therefore x / y = 3 / 5
Most Upvoted Answer
The sum of the numerator and denominator of a certain fraction is 8. ...
Problem Analysis:
Let's assume the fraction is represented as a/b, where a is the numerator and b is the denominator. According to the given information, the sum of the numerator and denominator is 8, so we have a + b = 8.
After adding 2 to both the numerator and the denominator, the new fraction is (a + 2)/(b + 2). The problem states that the value of the fraction increased by 4/35, so we have the equation:
(a + 2)/(b + 2) - a/b = 4/35
Solution:
To solve the equation, we can cross multiply and simplify:
35(a + 2) - 35a = 4(b + 2)
35a + 70 - 35a = 4b + 8
70 = 4b + 8
4b = 70 - 8
4b = 62
b = 62/4
b = 31/2
Now that we have the value of b, we can substitute it back into the equation a + b = 8 to find the value of a:
a + 31/2 = 8
a = 8 - 31/2
a = 16/2 - 31/2
a = -15/2
Therefore, the fraction is (-15/2)/(31/2), which simplifies to -15/31.
Final Answer:
The fraction is -15/31, which does not match any of the given answer options. Therefore, the correct answer is d) Cannot be determined.
Let's assume the fraction is represented as a/b, where a is the numerator and b is the denominator. According to the given information, the sum of the numerator and denominator is 8, so we have a + b = 8.
After adding 2 to both the numerator and the denominator, the new fraction is (a + 2)/(b + 2). The problem states that the value of the fraction increased by 4/35, so we have the equation:
(a + 2)/(b + 2) - a/b = 4/35
Solution:
To solve the equation, we can cross multiply and simplify:
35(a + 2) - 35a = 4(b + 2)
35a + 70 - 35a = 4b + 8
70 = 4b + 8
4b = 70 - 8
4b = 62
b = 62/4
b = 31/2
Now that we have the value of b, we can substitute it back into the equation a + b = 8 to find the value of a:
a + 31/2 = 8
a = 8 - 31/2
a = 16/2 - 31/2
a = -15/2
Therefore, the fraction is (-15/2)/(31/2), which simplifies to -15/31.
Final Answer:
The fraction is -15/31, which does not match any of the given answer options. Therefore, the correct answer is d) Cannot be determined.
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The sum of the numerator and denominator of a certain fraction is 8. If 2 is added to both the numerator and the denominator the value of the fraction increased by 4/35, then the fraction is:a)1/7b)3/5c)5/3d)Can not be determinedCorrect answer is option 'B'. Can you explain this answer?
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