Question

In a given fraction,if 1 is subtracted from the numerator and 2 is added to the denominator,it becomes $\frac{1}{2}$.if 7 is subtracted from the numerator and 2 is subtracted to the denominator,it becomes $\frac{1}{3}$.The fraction is

(a) $\frac{13}{24}$ (b) $\frac{15}{26}$ (c) $\frac{16}{27}$ (d) $\frac{16}{21}$

Answer 1

Let numerator be x and denominator be y.

Case 1
$\frac{x-1}{y+2}=\frac{1}{2}$
2x-2=y+2
y=2x-4.....(1)

Case 2:

$\frac{x-7}{y-2}=\frac{1}{3}$
3x-21=y-2
substitute the value of y from equation 1
3x-21=2x-4-2
3x-2x=21-4-2
x=15
put the value of x in equation 1
y=2(15)-4
y=26

fraction =x/y=15/26
option (b) 15/26 is correct answer.