Question

If two is added to the numerator of a fraction, it becomes 1 by2 and if 1 is subtracted from the denominator ,it becomes 1 by3. Find the fraction​

Answer 1

Answer:The original fraction will be 3/10

Step-by-step explanation:

Let the numerator be x

denominator be y

Original fraction = x/y

if 2 is added to the numerator of a fraction becomes 1/2

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

=> 2x + 4 = y

if 1 is subtracted from the denominator it becomes 1/3

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

=> 3x = y - 1

=> y = 3x + 1

equating both the above equation :

2x + 4 = 3x + 1

=> 3x - 2x = 4 - 1

=> x = 3

=> y = 3x + 1 = 9 + 1 = 10

Hence the original fraction will be 3/10.

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Answer 2

Answer:

The original fraction will be 3/10

Step-by-step explanation:

Let the numerator be x

and denominator be y

Original fraction = x/y

If 2 is added to the numerator of a fraction becomes 1/2

(x+2)/y = 1/2

(x+2)/y = 1/2=> 2x + 4 = y

=> y=2x + 4 ......(i)

If 1 is subtracted from the denominator it becomes 1/3

x/(y-1) = 1/3

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

/(y-1) = 1/3=> 3x = y - 1=> y = 3x + 1 ......(ii)

Equating both the above equations,we get,

2x + 4 = 3x + 1

2x + 4 = 3x + 1=> 3x - 2x = 4 - 1

2x + 4 = 3x + 1=> 3x - 2x = 4 - 1=> x = 3

y = 3x + 1

=>y= 9 + 1

=>y=10

Hence the original fraction will be 3/10.