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a_sh-v [17]
3 years ago
9

If 2 is added to both the numerator and denominator of a fraction its value becomes half. If two is subtracted from both the num

erator and denominator of the same fraction its value becomes 1/3. What is the original fraction"
Mathematics
1 answer:
Hitman42 [59]3 years ago
4 0

Answer:

The original fraction is \frac{6}{14}.

Step-by-step explanation:

Solution,

Let the fraction be'\frac{x}{y}'.

Where 'x' is the numerator and 'y' is the denominator.

Now according to question, if 2 is added to both the numerator and denominator the value of the fraction becomes 1/2.

So, framing the above sentence in equation form, we get;

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

On using cross multiplication method, we get;

2(x+2)=y+2\\\\2x+4=y+2\\\\2x+4-2=y\\\\\therefore\ y=2x+2\ \ \ \ equation\ 1

Now according to question, if 2 is Subtracted to both the numerator and denominator the value of the fraction becomes 1/3.

So, framing the above sentence in equation form, we get;

\frac{x-2}{y-2}=\frac{1}{3}

On using cross multiplication method, we get;

3(x-2)=y-2\\\\3x-6=y-2\\\\3x-y=-2+6\\\\3x-y=4 \ \ \ \ equation\ 2

Now Substituting the equation 1 in equation 1 we get;

3x-y=4\\\\3x-(2x+2)=4\\\\3x-2x-2=4\\\\3x-2x=4+2\\\\x=6

Now Substituting the value of x in equation 1 we get;

y=2x+2\\\\y=2\times6+2 = 14

Hence The original fraction is \frac{6}{14}.

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