Question

Q8. In a fraction's numerator is
increased by 1 and the denominator is
increased by 2 then the fraction
becomes 2/3. But when the numerator
is increased by 5 and the denominator
is increased by 1 then the fraction
becomes 5/4. What is the value of the
original fraction?
3/7
5/8
5/7
6/7​

Answer 1

Answer:

5/7

Step-by-step explanation:

let x & y be the original numerator and denominators resply.,

given, (x+1)/(y+2) = 2/3

    => 3(x+1) = 2(y+2)

    => 3x+3 = 2y+4

    => 3x-2y = 4-3

    => 3x-2y = 1  ---------- (1)

also, given, (x+5)/(y+1) = 5/4

    => 4(x+5) = 5(y+1)

    => 4x+20 = 5y+5

    => 4x-5y = 5-20

    => 4x-5y = -15  ---------- (2)

(2)*3 - (1)*4 => 12x-15y = -45

                   (-) 12x-8y  =   4

                             - 7y = -49

                             y = -49/ (-7)

                             y = 7

sustitute y=7 in (1),

=> 3x-2(7) = 1

=> 3x-14 = 1

=> 3x = 1+14

=> 3x = 15

=> x = 15/3

=> x = 5

so, the original fraction is 5/7