If 2 is added to the numerator of a fraction, it reduces to ( 1/2 ) an

1.	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 to ( 1/3 ). Find the fraction.
Answer» 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

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 to ( 1/3 ). Find the fraction.

Answer»

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