Question

the denominator of a fraction is 9 more than numerator if the numerator and denominator both is increased by 7 the new fraction becomes 7 /10 find the original fraction​

Answer 1

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Answer 2

Fraction:

Let x be one fraction.

Let y be another fraction.

From questions, y = x + 9

Now adding 7 on both numerator and denominator, we get,

$\bold{\frac{x+7}{y+7}=\frac{7}{10}}$

On substituting y equation, we get,

$\bold{\frac{x+7}{x+9+7}=\frac{7}{10}}$

$\bold{\frac{x+7}{x+16}=\frac{7}{10}}$

$\bold{10 x+70=7 x+96}$

$\bold{3 x=26}$

Thus, the value of x is:

$\bold{x=\frac{26}{3}}$

Now,

$\bold{y=\frac{26+27}{3}}$

The value of y is:

$\bold{y=\frac{53}{3}}$

Now, the original fraction is

$\bold{\frac{x}{y}=\frac{\left(\frac{26}{3}\right)}{\left(\frac{53}{3}\right)}}$

$\bold{\therefore\frac{x}{y}=\frac{26}{53}}$