Question

We add 1 to numerator and subtract 1 from the denominator a fraction becomes 1 . it also becomes 1/2 if we add 1 to the denominator , then the sum of the numerator and the denominator of the fraction is?

Answer 1

Answer:

${\pink{\boxed{\green{\sf{SUM\:OF\:NUMERATOR\:AND\:DENOMINATOR=8}}}}}$

Step-by-step explanation:

$\huge{\pink{\boxed{\green{\underline{\red{\sf{SOLUTION-}}}}}}}$

☆ Let numerator be x

☆ denominator be y

☆ Let the fraction be = x/y

☆ According to given information,

$\to \frac{x + 1}{y - 1} = 1 \\ \to x + 1 = y - 1 \\ { \boxed{\to x - y = - 2}} - - - - - (1) \\ \\ \to \frac{x}{y + 1} = \frac{1}{2} \\ \to 2x = y + 1 \\ { \boxed{\to 2x - y = 1}} - - - - - (2)$

☆ Using Substitution method:

$\to x - y = - 2 \\ \to x = - 2 + y - - - - - (3) \\ \\putting \: value \: of \: x \: in \: (2) \\ \to 2x - y = 1 \\ \to 2 \times ( - 2 + y) - y = 1 \\ \to - 4 + 2y - y = 1 \\ \to y = 1 + 4 \\ { \pink{ \boxed{ \green{\therefore y = 5}}}} \\ \\ putting \: value \: of \: y \: in \: (3) \\ \to x = - 2 + 5 \\ { \pink{ \boxed{ \green{\therefore x = 3}}}} \\ \\ { \pink{ \boxed{ \green{\therefore fraction= \frac{3}{5} }}}} \\ \\ { \pink{ \boxed{ \green{\therefore sum \: of \: numerator \: and \: denominator = 5 + 3 = 8}}}}$

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