Math, asked by modideepa32, 6 months ago

Form the pair of linear equations and find the solutoins (if they
exist) by the elemination method :
If we add 1 to the numerator and subtract 1 from the
denominator, a fraction reduces to 1. It becomes 1/2 if we only add 1 to the denominator. What is the fraction ?​

Answers

Answered by ekamjotkaur8055
1

Answer:

Step-by-step explanation:

Let the numerator be x.

Let the denominator be y.

The fraction is \frac{x}{y}

According to the Question:-

\frac{x+1}{y-1} = 1

=> x+1 = y-1 (cross multiplication)

=> x-y +2=0 (re-arranging the terms) -------------(1)

\frac{x}{y+1} =\frac{1}{2}

=> 2x = y+1 (cross multiplication)

=> 2x-y-1=0 (re-arranging the terms)--------------(2)

Subratricting (1) from (2)

x-3=0

=> x=3

Substituting x=3 in (1)

3-y+2=0

5-y=0

y=5

Hence the fraction is \frac{3}{5}

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Hope it helps !

Thanks

Answered by lakpar4ever
1

Answer:

Let x be the numerator of the fraction and y be the denominator of the fraction. Then the fraction is \frac{x}{y}.

Case I : When 1 is added to the numerator and 1 is subtracted from the denominator.

\frac{x+1}{y-1} = 1\\x+1 = 1(y-1)\\x+1 = y-1\\x-y = -2 \\x = y -2------------------------ (i)

Case II : When 1 is added to the denominator

\frac{x}{y+1} =\frac{1}{2} \\2x = 1(y+1)\\2x=y+1\\

Substituting the value of x from (i),

2(y-2) = y+1\\2y-4=y+1\\2y-y=1+4\\y=5

Substituting value of y in (i),

x=5-2\\x=3

Therefore the fraction is

\frac{x}{y} = \frac{3}{5} \\

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