Question

10. The numerator of a fraction is 2 less than the denominator. If 5 is added to both the mumerator
and the denominator, the fraction becomes
,
The fraction is​

Answer 1

Step-by-step explanation:

Let the denominator be x

Now according to the question.

Numerator is 2 less than denominator

= x - 2

x

5 added in both denominator and numerator

= x - 2 + 5

x + 5

= x + 3 {by simplifying}

x + 5

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Answer 2

Correct Question:

The numerator of a fraction is 2 less than the denominator. If 5 is added to both the numerator and the denominator, then the fraction becomes 3 / 4. Find the original fraction.

Answer:

The required fraction is 1 / 3.

Step-by-step-explanation:

Let the numerator of fraction be x.

And denominator of fraction be y.

∴ The fraction = x / y

From the first condition,

The numerator of a fraction is 2 less than the denominator.

∴ y = x + 2 - - - ( 1 )

From the second condition,

If 5 is added to both the numerator and the denominator, then the fraction becomes 3 / 4.

∴ ( x + 5 ) / ( y + 5 ) = 3 / 4

⇒ 4 ( x + 5 ) = 3 ( y + 5 )

⇒ 4x + 20 = 3y + 15

⇒ 4x - 3y = 15 - 20

⇒ 4x - 3 ( x + 2 ) = - 5 - - - [ From ( 1 ) ]

⇒ 4x - 3x - 6 = - 5

⇒ x = - 5 + 6

⇒ x = 1

∴ Numerator = 1

By substituting x = 1 in equation ( 1 ),

y = x + 2 - - - ( 1 )

⇒ y = 1 + 2

⇒ y = 3

∴ Denominator = 3

Now,

The fraction = Numerator / Denominator

⇒ The fraction = 1 / 3

∴ The required fraction is 1 / 3.