Question

The denominator of a rational number
is greater than its numerator by 7. If the
numerator is increased by 17 and the
denominator is reduced by 5, the obtained
number is a whole number 2. Find the
rational number.​

Answer 1

ᴀɴsᴡᴇʀ

• let the numerator be x
• then denominator is x + 7

$\bold{ \implies \: number = \frac{x }{x + 7} }$

and according to the question

( if the numerator is increased by 17 and the denominator is reduced by 5 , the obtained number is 2)

$\bold{: \implies \frac{(x )+ 17}{(x + 7) - 5} =2 } \: \: \: \: \: \\ \\ \bold{: \implies \frac{x + 17}{x + 7 - 5} = 2 } \: \: \: \: \: \: \: \: \\ \\ \bold{ : \implies \frac{x + 17}{x + 2} = 2 } \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ : \implies x + 17 = 2(x + 2) } \\ \\ \bold{ : \implies \: x + 17 = 2x + 4} \: \: \\ \\ \bold{ : \implies \: 17 - 4 = 2x - x } \: \\ \\ \bold{ : \implies \: \boxed{ \bold{ x = 13 }}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

so, numerator is 13

then, denominator is 13 + 7 = 20

$\bold{ \implies number = \frac{13}{13 + 7} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \boxed{ \red{ \bold{\frac{13}{20}} }}$

hence, the rational number is 13/20