Question

if the numerator of the fraction is increased by 40% and the denominator is increased by 50% and the resultant fraction is 2/5.What is the original fraction​

Answer 1

Answer:

20/10 is the original fraction

Answer 2

Answer

Let the numerator be x.

Let the denominator be y.

Let the original fraction be $\sf \dfrac{x}{y}$

According to the question,

$\sf \dashrightarrow \dfrac{x + 40\% \: of \: x}{y + 50\% \: of \: y} = \dfrac{2}{5}$

$\sf \dashrightarrow \dfrac{x + \dfrac{40}{100} \times x}{y + \dfrac{50}{100} \times y} = \dfrac{2}{5}$

$\sf \dashrightarrow \dfrac{x + \dfrac{40x}{100}}{y + \dfrac{50y}{100}} = \dfrac{2}{5}$

$\sf \dashrightarrow \dfrac{x + \dfrac{2x}{5}}{y + \dfrac{1y}{2}} = \dfrac{2}{5}$

$\sf \dashrightarrow \dfrac{\dfrac{5x + 2x}{5}}{\dfrac{2y + 1y}{2}} = \dfrac{2}{5}$

$\sf \dashrightarrow \dfrac{\dfrac{7x}{5}}{\dfrac{3y}{2}} = \dfrac{2}{5}$

$\sf \dashrightarrow \dfrac{x}{y} = \dfrac{2}{5} \times \dfrac{3}{2} \times \dfrac{5}{7}$

$\sf \dashrightarrow \dfrac{x}{y} = \dfrac{1}{1} \times \dfrac{3}{1} \times \dfrac{1}{7}$

$\sf \dashrightarrow \dfrac{x}{y} = \dfrac{3}{7}$

Hence, the original fraction is $\sf \dfrac{3}{7}$.