Question

the denominator of a rational number is greater than its numerator by 6. If the numerator is decreased by 1 , the denominator is increased by 1 , the number obtained is 1/3 . Find the rational number. ​

Answer 1

$\;\;\underline{\textbf{\textsf{ Given:-}}}$

• If 1 is subtracted from the numerator and 1 is added to the denominator, the number becomes 1/3.

$\;\;\underline{\textbf{\textsf{ To Find :-}}}$

• What's the fraction?

$\;\;\underline{\textbf{\textsf{ Solution :-}}}$

Let the numerator be a and Denominator be (a + 6).

Then, the fraction will be

$= \sf\dfrac{a}{a+6}$

Given that,

• If 1 is subtracted from the numerator and 1 is added to the denominator, the number becomes 1/3.

A.T.Q :-

$\dashrightarrow \sf \dfrac{Numerator-1}{Denominator+1}=\dfrac{1}{3}\\\\\\\dashrightarrow \sf \dfrac{a-1}{(a+6)+1}=\dfrac{1}{3}\\\\\\\dashrightarrow \sf \dfrac{a-1}{a+7}=\dfrac{1}{3}\\\\\\\dashrightarrow \sf 3(a - 1) = 1(a + 7)\\\\\\\dashrightarrow \sf 3a - 3 = a + 7\\\\\\\dashrightarrow \sf 3a -a = 7 + 3\\\\\\\dashrightarrow \sf 2a= 10\\\\\\\dashrightarrow \sf a = \dfrac{10}{2}\\\\\\\dashrightarrow \sf a = 5$

Then, the fraction will be

$= \sf\dfrac{a}{a+6}$

$= \sf\dfrac{5}{11}$

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