Question

the sum of numerator and denominator of a given fraction is 12 . if the denominator is increased by 3 then the fraction becomes 1/2. find the fraction​

Answer 1

Step-by-step explanation:

Given :-

The sum of numerator and denominator of a given fraction is 12 . if the denominator is increased by 3 then the fraction becomes 1/2.

To find :-

Find the fraction ?

Solution :-

Let the numerator be X

Let the denominator be Y

Then , the fraction = X/Y

Given that

The sum of the numerator and the denominator = 12

X+Y = 12---------(1)

If the denominator is increased by 3 then the fraction = X/(Y+3)

Given that

If the denominator is increased by 3 then the fraction becomes 1/2.

=> X/(Y+3) = 1/2

On applying cross multiplication then

=> 2X = Y+3

=> 2X-Y = 3 ----------(2)

On adding (1) &(2)

X + Y = 12

2X - Y = 3

(+)

_________

3X + 0 = 15

_________

=> 3X = 15

=>X = 15/3

=> X = 5

On Substituting the value of X in (1) then

=> 5+Y = 12

=> Y = 12-5

=>Y = 7

Therefore, X = 5 and Y = 7

The numerator = 5

The denominator = 7

Answer:-

The required fraction for the given problem is 5/7

Check:-

The fraction = 5/7

Numerator+Denominator = 5+7=12

Denominator+3 =7+3 = 10

Then the fraction = 5/10 = 1/2

Verified the given relations in the given problem.