The denominator of a rational number is 1 more than the numerator. If

1.	The denominator of a rational number is 1 more than the numerator. If the numeratoris reduced by 2 and denominator is increased by 3, the rational no. reduces to ¼. Find the rational number
Answer» SOLUTION :- LET, Numerator = x Denominator = y According to the FIRST condition, $\longrightarrow\sf y= x+<klux>1</klux> \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ........................(1)$ According to the SECOND condition, $\longrightarrow\sf \dfrac{x-2}{y+3}=\dfrac{1}{4} \\\\\longrightarrow\sf 4(x-2)=y+3 \\\\\longrightarrow 4x-8 = y+3 \\\\\longrightarrow 4x-y = 3+8 \\\\\longrightarrow 4x-y = 11 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ........................(2)$ Substitute y = x + 1 in EQUATION (2), $\longrightarrow\sf 4x-(x+1)=11\\\\\longrightarrow 4x-x-1= 11 \\\\\longrightarrow 3x= 12 \\\\\longrightarrow \bf x = 4$ Numerator = 4 Denominator = 4 + 1 = 5 $\bf FRACTION = \dfrac{4}{5}$

The denominator of a rational number is 1 more than the numerator. If the numeratoris reduced by 2 and denominator is increased by 3, the rational no. reduces to ¼. Find the rational number

Answer»

SOLUTION :-

Numerator = x

Denominator = y

According to the FIRST condition,

$\longrightarrow\sf y= x+<klux>1</klux> \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ........................(1)$

According to the SECOND condition,

$\longrightarrow\sf \dfrac{x-2}{y+3}=\dfrac{1}{4} \\\\\longrightarrow\sf 4(x-2)=y+3 \\\\\longrightarrow 4x-8 = y+3 \\\\\longrightarrow 4x-y = 3+8 \\\\\longrightarrow 4x-y = 11 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ........................(2)$