A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. The fraction obtained is:a.3/10b.4/7c.5/12d.6/13
Question
A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. The fraction obtained is:a.3/10b.4/7c.5/12d.6/13
Solution
Let's denote the numerator as x and the denominator as y.
From the problem, we have two equations:
- x - 1 = 1/3 * y (because the fraction becomes 1/3 when 1 is subtracted from the numerator)
- x = 1/4 * (y + 8) (because the fraction becomes 1/4 when 8 is added to the denominator)
We can rewrite these equations as:
- 3x - y = 1
- 4x - y = 8
Subtracting the first equation from the second gives us x = 7.
Substituting x = 7 into the first equation gives us 3*7 - y = 1, which simplifies to y = 20.
So, the fraction is 7/20, which is not one of the options given. There seems to be a mistake in the problem or the answer choices.
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