Question

we onginal numbers.
4. The denominator of a rational number is less than its numerator than 5.1f 5 is added to the numerator,
the new number becomes
11/6 . Find the original rational number. ​

Answer 1

SOLUTION :-

Let,

Numerator = x

Denominator = y

According to the first condition,

$\longrightarrow\sf y=x-5 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ............................(1)$

According to the second condition,

$\longrightarrow\sf \dfrac{x+5}{y}=\dfrac{11}{6} \\\\\longrightarrow 6(x+5)=11y \\\\\longrightarrow 6x+30=11y \\\\\longrightarrow 6x-11y = -30 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ............................(2)$

Substitute y = x - 5 in equation (2),

$\longrightarrow \sf 6x-11(x-5)=-30\\\\\longrightarrow 6x-11x+55 =-30 \\\\\longrightarrow 6x-11x=-30-55\\\\\longrightarrow -5x=-85 \\\\\longrightarrow 5x= 85 \\\\\longrightarrow \bf x = 17$

$\bf Original \ rational \ number = \dfrac{17}{12}$

Answer 2

Question :-

the denominator of a rational number is less than its numerator than 5 if I was added to the numerator the new number becomes 11/6 find the original rational number ?

Answer :-

Given :-

• the denominator of a rational number is less than its numerator than 5
• if it is added to numerator the new number becomes 11/6

what we have to find here ?

=> we have to find here the original rational number

Solution :-

let's here numerator be - "x" .

and the denominator be - "y"

according to the given question , In 1st case ;

y=x-5

and in the second case ;

x+5/y=11/6

=> 6(x+5)=11y

=> 6x +30=11y

=> 6x-11y=-30

now putting the value in the equation (y=x-5) in the case-2 , we get ;

=> 6 x - 11 (x-5)= -30

=> 6x-11x+55=-30

=>6x-11x=-30-55

=>-5x=-85

∆ here the subtraction will be cancelled both the sides .

=> 5x=85

∆ now dividing 85 with 5 we get ;

=> x=85/5=17

So, the original number will be 17 / 12 .