Question

Denominators of a fraction is 9 more than its numerators. If the numerator and denominator both are increased by 7 the two fractions become 7/10. Find the original fraction.

Answer 1

Let the numerator of the fraction be x.

According to the question,

The original fraction = x / x + 9

Then, x + 7/ x + 9 + 7 = 7/10

or, x + 7 / x + 16 = 7/10

or, 10 ( x + 7 ) = 7 ( x + 16 )

or, 10x + 70 = 7x + 112

or, 10x - 7x = 112 - 70

or, 3x = 42

or, x = 42/3

or, x = 14

So, the numerator of the original fraction is 14 and the denominator is x + 7 = 14 + 7 = 21.

The original fraction is 14/21 .

Answer 2

Answer:

$Let \: numerator \: be \: 'x' \\ </p><p>Then \: Denominator=x+9 \\ </p><p>Fraction= \frac{x}{x + 9} \\ \frac{x + 7}{x + 9 + 7} = \frac{7}{10} \\ 10(x + 7) = 7( x+ 16) \\ 10x + 70 = 7x + 112 \\ 10x - 7x = 112 - 70 \\ 3x = 42 \\ x = 14$

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