Question

the denominator of a rational number is 1 greater than its numerator if the numerator is increased by 17 and the denominator is decreased by 1 the number become 27 find the rational number​

Answer 1

Let the required rational number be ( p / q )

q = p + 1

Now ,

New number -

=> ( p + 17 ) / ( q + 1 ) = 27

=> ( p + 17 ) / ( p + 2 ) = 27

=> 27p + 54 = p + 17

=> 26p = - 37

=> p = ( -37 / 26 )

=> q = ( - 11 / 26 )

Required rational no -

=> ( 37 / 11 )

This is the required answer ...

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Answer 2

$\huge\sf\pink{Answer}$

☞ Your Answer is (37/11)

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ The denominator of a rational number is 1 greater than its numerator

✭ If the number is increased by 17 and the denominator by 1 the new number becomes 27

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

◈ The rational number?

$\rule{110}1$

$\huge\sf\purple{Steps}$

Let the rational number be $\sf \dfrac{a}{b}$

≫ $\sf a = b + 1$

Now , the New Number will be,

➝ $\sf\dfrac{a+17}{b +1} = 27$

➝ $\sf\dfrac{a+17}{b+2} = 27$

➝ $\sf 27a+54 =b + 17$

➝ $\sf 26a = - 37$

➝ $\sf a= \dfrac{-37}{26}$

➝ $\sf b= \dfrac{-11}{26}$

Therefore the number will be,

$\sf\orange{Number = \dfrac{37}{11}}$

$\rule{170}3$