If 2 is added to the numerator
of a fraction, it reduces to 1/2 and
if 1 is subtracted from the denominator, it reduces

1 thought on “If 2 is added to the numerator<br />of a fraction, it reduces to 1/2 and<br />if 1 is subtracted from the denominator, it reduces”

1. Let the required fraction be x/y .

   Then, we have: x+2/y = 1/2

   ⇒ 2(x + 2) = y

   ⇒ 2x + 4 = y

   ⇒2x – y = -4 ……(i)

   Again, x/y−1 = 1/3

   ⇒3x = 1(y – 1)

   ⇒3x – y = -1 ……(ii)

   On subtracting (i) from (ii),

   we get: x = (-1 + 4) = 3

   On substituting x = 3 in (i),

   we get: 2 × 3 – y = -4

   ⇒ 6 – y = -4

   ⇒ y = (6 + 4) = 10

   ∴ x = 3 and y = 10

   Hence, the required fraction is 3/10

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