When 8 is added to the numerator of a fraction and 12 is added to its denominator, the fraction becomes 1/2. When 2 is subtracted from its numerator and denominator, the fraction becomes 1/8. Find the original fraction.
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Correct answer: B
Explanation
The correct answer is option 2 i.e. 3/10.
Let the fraction be x/y.
According to the question;
⇒ (x + 8)/(y + 12) = 1/2
⇒ 2x - y = -4 ----- (1)
Now,
⇒ (x - 2)/(y - 2) = 1/8
⇒ 8x - y = 14 ---- (2)
Equating: (2) - (1), we get
⇒ 8x - y - 2x + y = 14 + 4
⇒ 6x = 18
⇒ x = 3 and y = 10
Hence, the original fraction = 3/10