The numerator of a fraction is 5 less than the denominator. If 1 is added to both the numerator and the denominator, the fraction would become 2/3. Find the fraction?
- 15/31
- 3/14
- 9/14
- None of these
Explanation
Let's denote the denominator as x. Then, the numerator is x - 5.
Original fraction: (x - 5)/x
After adding 1 to both numerator and denominator:
New fraction: (x - 5 + 1)/(x + 1) = (x - 4)/(x + 1)
Given that the new fraction is 2/3:
(x - 4)/(x + 1) = 2/3
Cross-multiply:
3(x - 4) = 2(x + 1)
Expand and solve:
3x - 12 = 2x + 2
x = 14
So, the original fraction is:
(x - 5)/x = (14 - 5)/14 = 9/14
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