Question

Amazing Question :



1) A fraction becomes 2/5 when 2 is subtracted from the numerator and denominator it becomes 3/4 when 5 is added to its denominator and numerator, find the fraction.

Answer 1

The fraction is 4/7

REFER TO THE ATTACHMENT FOR THE ANSWER

Corrected my mistake

Answer 2

Given,

• A fraction in which if we subtracted 2 from numerator and denominator so fraction becomes 2/5 .
• A fraction in which if we add 5 to numerator and denominator then fraction becomes 3/4.

To Find,

• The fraction after all this conditions .

Solution,

⇒Suppose the numerator be x and Denominator be y

Therefore ,

Original Fraction = $\bold{\frac{x}{y}}$

$\boxed{\bold{\red{According \ to \ the \ First \ Condition :}}}$

$\implies \bold{\frac{x - 2}{y - 2} = \frac{2}{5}}}$

$\implies \bold{5(x - 2) = 2(y - 2)}$

$\implies \bold{ 5x - 10 = 2y - 4}$

$\implies \bold{5x - 2y =6}$

$\implies \boxed{\bold{ x = \frac{6 + 2y}{5}}}$.......1) Equation

$\boxed{\bold{\red{According \ to \ the \ Second \ Condition :}}}$

$\implies \bold{\frac{x + 5}{y + 5} = \frac{3}{4}}$

$\implies \bold{4(x + 5) = 3(y + 5)}$

$\implies \bold{4x + 20 = 3y + 15}$

$\bold{\implies 4x - 3y = -5}}$............2) Equation

Now put value of x from First Equation :-

$\implies \bold{ 4 \big(\big} \bold{\frac{6 + 2y}{5} \big)\big} - 3y = -5$

$\implies \bold{\frac{24 + 8y}{5} - 3y = -5}$

$\implies \bold{\frac{24 + 8y - 15y }{5} = -5}$

$\implies \bold{24 - 7y = -5 \times 5}$

$\implies \bold{-7y = -25 - 24}$

$\implies \bold{ -7y = -49}$

$\implies \bold{ y = \frac{-49}{-7}}$

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

Now Put the value of y in Equation 2) :-

$\implies \bold{ 4x - 3y = -5}$

$\implies \bold{ 4x - 3(7) = -5}$

$\implies \bold{4x - 21 = -5}$

$\implies \bold{ 4x = -5 + 21}$

$\implies \bold{ 4x = 16}$

$\implies \boxed{\bold{ x = 4}}$

Therefore ,

The Fraction $= \bold{\frac{4}{7}}$

$\rule{200}2$