Question

A fraction becomes 1/2,if 2 is added to both numerator and denominator. If 3 is added to both numerator and denominator it becomes 5/6​

Answer 1

Answer:

$\frac{\frac{-7}{4} }{\frac{-3}{2} }$

Step-by-step explanation:

let p/q be the fractional number,

given, (p+2)/(q+2) = 1/2

     =>  2(p+2) = q+2

     =>  2p+4 -q = 2

     => 2p - q = 2-4 = -2

     => 2p-q = -2 --------------------------- (1)

also, given that (p+3)/(q+3) = 5/6

=> 6(p+3) = 5(q+3)

=> 6p + 18 = 5q +15

=> 6p - 5q = 15-18

=> 6p -5q = -3  --------------------------- (2)

3 x (1)  - (2)   => 6p - 3q = -6

                    (-) 6p - 5q = -3

                                 2q = -3

                                    q = -3/2

substitute q = -3/2 in (1), gives

2p - (-3/2) = -2

=> 2p + (3/2) = -2

=> 4p + 3 = -4

=> 4p = -4-3 = -7

=> p = -7/4

so, the required fraction =  p/q = $\frac{\frac{-7}{4} }{\frac{-3}{2} }$