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in Mathematics by (33.0k points)

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.

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Best 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

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