Question

The sum of the numerator and denominator of a fraction is 12. If 1 is added to both the

numerator and the denominator, the fraction becomes

3/4

.



Find the fraction​

Answer 1

Nice question! You have to substitute the value! HOPE IT HELPED

Answer 2

★ ${\underline{\underline{\purple{\bold{Given:-}}}}}$

• The sum of the numerator and the denominator of a fraction is 12.
• If 1 is added to both the numerator and denominator , the fraction becomes 3/4.

★ ${\underline{\underline{\purple{\bold{To\:find:-}}}}}$

• The original fraction.

★ ${\underline{\underline{\purple{\bold{Solution:-}}}}}$

Consider,

• Numerator = x
• Denominator = y

${\green{\underline{\bold{According\:to\:the\:1st\: condition:-}}}}$

• The sum of the numerator and the denominator of a fraction is 12.

$\to\sf{x+y=12}$

$\to\sf{x=12-y...............(1)}$

${\green{\underline{\bold{According\:to\:the\:2nd\: condition:-}}}}$

• If 1 is added to both the numerator and denominator , the fraction becomes 3/4.

$\to\sf{\dfrac{x+1}{y+1}=\dfrac{3}{4}}$

$\to\sf{\dfrac{12-y+1}{y+1}=\dfrac{3}{4}\:[put\:x=12-y]}$

$\to\sf{\dfrac{13-y}{y+1}=\dfrac{3}{4}}$

$\to\sf{52-4y=3y+3}$

$\to\sf{-4y-3y=3-52}$

$\to\sf{-7y=-49}$

$\to\sf{y=7}$

• Denominator = 7

Now put y=7 in eq(1) for getting the value of x.

$\to\sf{x=12-y}$

$\to\sf{x=12-7}$

$\to\sf{x=5}$

• Numerator = 5

Therefore,

${\boxed{\bold{Original\: Fraction\:=\dfrac{5}{7}}}}$