Question

If 2 added to a numerator of a fraction it becomes ⅕, if 2 is taken from the denominator it becomes ⅐. Find the fraction​

Answer 1

Answer:

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Answer 2

Solution :-

Let,

Numerator = x

Denominator = y

According to the first condition :-

$\longrightarrow \sf \dfrac{x+2}{y}= \dfrac{1}{5} \\\\\longrightarrow 5(x+2) = y \\\\\longrightarrow 5x+10 = y \\\\\longrightarrow 5x - y = -10 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ......................(1)$

According to the second condition :-

$\longrightarrow \sf \dfrac{x}{y-2}= \dfrac{1}{7} \\\\\longrightarrow 7x =1(y-2) \\\\\longrightarrow 7x = y - 2 \\\\\longrightarrow 7x-y = -2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ......................(2)$

Eq (2) - Eq (1) :-

$\longrightarrow \sf 2x = 8 \\\\\longrightarrow \bf x = 4$

Substitute the value of x in eq (2) :-

$\longrightarrow \sf 5 \times 4 - y = - 10 \\\\\longrightarrow 20 - y = - 10 \\\\\longrightarrow -y = -10 - 20 \\\\\longrightarrow -y = - 30 \\\\\longrightarrow \bf y = 30$

$\bf FRACTION = \dfrac{4}{30}$