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 numerator is 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, $\longrightarrow\sf y= x+1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ........................(1)$ According to the second condition, $\longrightarrow\sf \dfrac{x-<klux>2</klux>}{y+3}=\dfrac{1}{<klux>4</klux>} \\\\\longrightarrow\sf 4(x-2)=y+3 \\\\\longrightarrow 4x-8 = y+3 \\\\\longrightarrow 4x-y = 3+8 \\\\\longrightarrow 4x-y = 11 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ........................(2)$ 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 numerator is reduced by 2 and denominator is increased by 3, the rational no. reduces to ¼. Find the rational number

Answer»

SOLUTION :-

Let,

Denominator = y

According to the first condition,

$\longrightarrow\sf y= x+1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ........................(1)$

According to the second condition,

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

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

$\bf FRACTION = \dfrac{4}{5}$