In a given fraction, if 1 subtracted from the numerator and 2 is added to the denominator, it becomes ` (1)/(2)`. If 7 is subtracted from the numerator and 2 is subtracted from the denominator, it becomes `(1)/(3)`. The fraction is

Options

A. ` (13)/(24)`
B. `(15)/(26)`
C. `(16)/(27)`
D. `(16)/(21)`

Answer

B

Explanation

Let the required fraction be `(x)/(y)`. Then,
` ( x - 1)/( y + 2) = (1)/(2)rArr 2 x - 2 = y + 2 rArr 2x - y = 4" " `... (i)
`( x - 7)/( y - 2 ) = (1)/(3) rArr 3x - 21 = y - 2 rArr 3x - y = 19`.