Question

the denominator of a rational number is greater than its numerator by 7 if the numerator is increased by 17 and the denominator decreased by 6 the new number become to find the original number answer

Answer 1

$\bf Answer :$

The original fraction is 15 / 22.

$\bf Step-by-step \: explanation :$

Let the number be x,
And, denominator = x + 7.

According to the question ;

$\sf \frac{x + 17}{x + 7 - 6} = 2 \\ \\ \sf \frac{x + 17}{x + 1} = 2 \\ \\ \sf x + 17 = 2x + 2 \\ \\ \sf x - 2x = 2 - 17 \\ \\ \sf - x = - 15 \\ \\ \sf x = 15$

Hence,

$\text{fraction} = \frac{x }{x + 7} \\ \\ \text{fraction} = \frac{15}{15 + 7} \\ \\ \text{fraction} = \frac{15}{22} \: \: \: \: \: \:$

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Thanks for the question !

Answer 2

Solutions :-

Given

When numerator is increase by 17 and denominator is decreased by 6 then fraction become 2

Let number be x

A/q

$\frac{x + 17}{(x + 7) - 6} = 2 \\ \\ \frac{x + 17}{x + 1} = 2 \\ \\ x + 17 = 2x + 2 \\ - 2x + x = 2 - 17 \\ - x = - 15 \\ x = 15$
Hence

Oroginal Number is ⤵

$\frac{x}{x + 7} = \frac{15}{15 + 7} = \frac{15}{22}$

Thanks

@Anushka