Question

the denominator of fraction is 2 more than the numerator. If 3 is added to both, numerator and the denominator, the fraction becomes 3/4 . what is the fraction​

Answer 1

Step-by-step explanation:

Given :-

The denominator of fraction is 2 more than the numerator.If 3 is added to both, numerator and the denominator, the fraction becomes 3/4 .

To find :-

What is the fraction?

Solution :-

Let the numerator of a fraction be X

Then the denominator = 2 more than the numerator.

=> Denominator = Numerator + 2

=> Denominator = X+2

Now the Original Fraction = X/(X+2) ----(1)

If 3 is added to both numerator and the denominator then it becomes

=> (X+3)/(X+2+3)

=> (X+3)/(X+5)

According to the given problem

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

=> (X+3)/(X+5) = 3/4

On applying cross multiplication then

=> 4(X+3) = 3(X+5)

=> 4X+12 = 3X+15

=> 4X-3X = 15-12

=> X = 3

=> Numerator = 3

Denominator = Numerator + 2

=> Denominator = 3+2 = 5

Fraction = Numerator/Denominator

Fraction = 3/5

Answer:-

The Original Fraction for the given problem is 3/5

Check :-

Fraction = 3/5

Denominator = 3+2 = 5

Denominator = Numerator + 2

If 3 is added to both, numerator and the denominator, the fraction becomes

=> (3+3)/(5+3)

=> 6/8

=> 3/4

Verified the given relations in the given problem.

Used formula:-

Fraction = Numerator / Denominator