Question

. If the numerator of a fraction is decreased by 1 it becomes 2/3. When the
denominator is increased by 5 it becomes 1/2 . What is the fraction?​

Answer 1

Answer:

Let the numerator and denominator of the required fraction be x and y respectively.

Then the required fraction will be ; x/y

according to question;

case 1:

When the numerator of the fraction is decreased by 1 , then it becomes 2/3.

ie,

=> (x-1)/y=2/3

=> 3(x-1)=2y

=> 3x-3=2y -------(1)

case 2:

when the denominator of the fraction is increased by 5, then it becomes 1/2.

ie,

=> x/(y+5)=1/2

=> 2x=y+5

=> y=2x-5 --------(2)

now,

putting the value of y=2x-5 in eq-(1)

we get,

=> 3x-3=2(2x-5)

=> 3x-3=4x-10

=> 4x-3x=10-3

=> x=7

now,

using eq-(2),

we have,

=> y=2x-5

=> y=2(7)-5

=> y=14-5

=> y=9

Thus, the required Fraction is: x/y

ie, 7/9.