Question

the Numerator of a fraction is less than it denominator by 8 when one is added to the numerator and 2 is subtracted from the denominator,the fraction obtained is 2/7 find the original fractio
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Answer 1

Answer:

Let denominator of fraction be X. Fraction = Numerator/Denominator = ( X -8)/X. According to question, When 1 is added to numerator and 2 is subtracted from denominator the fraction obtained is 2/7.

Answer 2

Given :

• The numerator of a fraction is less than its denominator by 8.

• If 1 is added to the numerator and 2 is subtracted from the denominator the fraction we will get is 2/7.

To find :

The fraction after following the given situations.

Solution :

Let's assume that :

Denominator = x

Then,

Numerator will be (x - 8)

Fractional form :

$\longrightarrow\sf \frac{(x - 8)}{x}$

Now,

Addition of 1 in numerator :

➠ (x - 8) + 1

And also Subtraction of 2 in the denominator :

➠ (x - 2)

New fraction formed :

$\longrightarrow\sf \frac{(x - 8) + 1}{x - 2}$

$☯ \begin{gathered}\underline{\boldsymbol{According\: to \:the\: question :}}\\\end{gathered}$

$\longrightarrow \sf \frac{(x - 8) + 1}{x - 2} = \frac{2}{7} \: \sf \gray{(cross \: multiplication)}$

$\longrightarrow\sf 7 \{ (x - 8) + 1\} = 2(x - 2)$

$\longrightarrow\sf 7 \{ x - 7\} = 2x - 2$

$\longrightarrow\sf 7x - 49 = 2x - 2$

$\longrightarrow\sf 7x - 2x = 49 - 2$

$\longrightarrow\sf 5x = 45$

$\longrightarrow\sf x = \frac{ \cancel{45}}{ \cancel 5}$

$\longrightarrow\sf \: x = 9$

After solving this we get :

x = 9

Numerator = (x - 8) = 1

And, Denominator = x = 9 ans.

$\therefore$ The original fraction will be :

$<strong> </strong> \sf \longmapsto \: Required \: \: fraction = \frac{1}{9} \ ans.$

Hence, we are done.