Question

Numerator of a fraction is 2 less than the denominator. if 1 is added to the numerator and 3 to the denominator than the fraction becomes 2by3.find the original fraction.

Answer 1

Given :

Let Denominator be ' D '

Numerator = D - 2 .

1 is added to N and 3 is added to D :

Actual N = D - 2 + 1 = D - 1.

Actual D = D + 3 .

According to the question:

D - 1 / D + 3 = 2 / 3 cross multiply

= 3 ( D - 1 ) = 2 ( D + 3 )

= 3D - 3 = 2D - 6

= 3D - 2D = 6 + 3

= D = 9

so, Denominator = 9

Numerator = D - 2

N = 9 - 2

N = 7

Original fraction :

= 7 / 9

.

Answer 2

Step-by-step explanation:

Given -

• Numerator of fraction is 2 less than the denominator.
• If 1 is added to the numerator and 3 to the denominator than the fraction becomes 2/3

To Find -

• The original fraction

Let y be the denominator.

Then,

According to question :-

• Numerator = y - 2

Now,

If 3 is added to the denominator

It means,

• New denominator = y + 3

And

If 1 is added to the numerator

It means,

• New numerator = y - 2 + 1 = y - 1

Now, According to the question :-

• The fraction becomes 2/3

It means,

⇝y - 1/y + 3 = 2/3

⇝3(y - 1) = 2(y + 3)

⇝3y - 3 = 2y + 6

⇝3y - 2y = 9

⇝y = 9

Then,

Numerator = y - 2 = 9 - 2 = 7

Therefore,

The original fraction is 7/9.