Question

If 2 is subracted to the numerator and one is added to the denominator, a fraction becomes 1/2, but when 4 is added to numerator and 3 is subarctic from denominator, the fraction becomes 3/2.find the fraction

Answer 1

Let the fraction be a/b

According to first condition,

(a-2) / (b+ 1) = 1 / 2

=> 2a - 4 = b + 1

=> 2a - b = 5 -------(1)

According to second condition,

(a + 4) / ( b - 3) = 3 / 2

=> 2a + 8 = 3b - 9

=> 3b - 2a = 17 ------(2)

On adding equation 1 and 2, we get

2b = 22

=> b = 11

Now,

On putting the value of b in equation 1, we get

2a - 11 = 5

=> 2a = 16

=> a = 8

Required fraction = 8/ 11