The denominator of a rational number is greater than its numerator by

1.	The denominator of a rational number is greater than its numerator by 7. If thenumerator is increased by 17 and denominator decreased by 6, the new numberbecomes 2. Find the original number?
Answer» Given :- The denominator of a RATIONAL number is greater than its numerator by 7. If the numerator is increased by 17 and denominator DECREASED by 6,the new number becomes 2. To find :- The original number Solution :- Let the numerator of rational number be x and denominator of rational number be x + 7 ⪼ Numerator is increased by 17, (x + 17) ⪼ Denominator is decreased by 6, (x + 7) - 6 According to the Question, $\rm\:\dfrac{x+17}{(x+7)-6}=2$ $\rm\longrightarrow\:\dfrac{x+17}{x-1}=2$ By cross multiplication, $\rm\longrightarrow\:x+17=2(x+1)$ $\rm\longrightarrow\:x+17=2x+2$ $\rm\longrightarrow\:x-2x=2-17$ $\rm\longrightarrow\:\cancel{-}x=\cancel{-}<klux>15</klux>$ $\rm\longrightarrow\:x=15$ THEREFORE,the numerator will be 15, And Denominator = x + 7 Denominator = 15 + 7 Denominator = 22 Hence,the original number will be15/22.

The denominator of a rational number is greater than its numerator by 7. If thenumerator is increased by 17 and denominator decreased by 6, the new numberbecomes 2. Find the original number?

Answer»

If the numerator is increased by 17 and denominator DECREASED by 6,the new number becomes 2.

Let the numerator of rational number be x

and denominator of rational number be x + 7

⪼ Numerator is increased by 17,

⪼ Denominator is decreased by 6,

According to the Question,

$\rm\:\dfrac{x+17}{(x+7)-6}=2$

$\rm\longrightarrow\:\dfrac{x+17}{x-1}=2$

By cross multiplication,

$\rm\longrightarrow\:x+17=2(x+1)$

$\rm\longrightarrow\:x+17=2x+2$

$\rm\longrightarrow\:x-2x=2-17$

$\rm\longrightarrow\:\cancel{-}x=\cancel{-}<klux>15</klux>$

$\rm\longrightarrow\:x=15$

THEREFORE,the numerator will be 15,

And Denominator = x + 7

Denominator = 15 + 7

Denominator = 22

Hence,the original number will be15/22.