Question

Sum of the numerator and denominator of a fraction is 12. If denominator is increased by 3,the fraction becomes 1/2. Find the fraction

Answer 1

Given,

• Sum of the numerator and denominator of a fraction is 12 .
• If denominator is increased by 3 then the fraction becomes 1/2

To Find,

• The Fraction

Solution,

⇒Suppose the numerator be x

And , Suppose the denominator be y

According to the First Condition :-

• Sum of the numerator and denominator of a fraction is 12 .

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

$\implies \boxed{\sf{ x = 12 - y}}$

According to the Second Condition :-

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

$\implies \sf{\dfrac{x}{y + 3} = \dfrac{1}{2}}$

$\implies \sf{2x = y + 3}$

$\implies \sf{2( 12 - y) = y + 3}$

(Put the value of x from the First Condition )

$\implies \sf{24 - 2y = y + 3}$

$\implies \sf{24 - 3 = y + 2y}$

$\implies \sf{21 = 3y}$

$\implies \sf{y = \dfrac{21}{3}}$

$\implies \boxed{\sf{ y = 7}}$

Now Put value of x in First Condition :-

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

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

$\implies \boxed{\sf{ x = 5}}$

Therefore ,

$\boxed{\sf{\red{ The \ Fraction = \dfrac{5}{7}}}}$

$\rule{200}2$

Answer 2

Answer:5/7

Step-by-step explanation:let the numerator be x

let the denominator be y

fraction=x/y

equation 1

x+y=12

if the denominator is increased by

[y+3] the fraction will be

x/y+3=1/2

cross multiply

2x=y+3

y=2x-3 [equation 2]

substitute the value of y

x+2x-3=12

x=5

y=7