Question

The denominator of a rational number is greater than its numerator by 6. If the numerator is increased by 1 and the denominator is decreased by 3, the number obtained is 6/7. Find the rational number

Answer 1

Answer:

11/17

Step-by-step explanation:

let the numerator be x then denominator will be (x + 6)

so ATP,

x  +  1     =    6

x+6-3           7

x  +  1     =    6

x  +  3           7

7x + 7 =  6x + 18                                         (cross multiplication)

7x - 6x = 18 - 7

x = 11

then the rational no. will be =  x/(x+6) = 11/(11+6) = 11/17

Answer 2

${\boxed{\tt{Answer:}}}$

Let the numerator be x

Then, Denominator = x+6

$\implies$ It is given that numerator is increased by 1 and the denominator is decreased by 3

$\therefore$Numerator of new rational number = x+1

$\therefore$Denominator of new rational number = (x+6)-3 = x+3

$\therefore$ New rational number =$\frac{x+1}{x+3}$

But the new rational number given as $\frac{6}{7}$

$\therefore\frac{x+1}{x+3}={6}{7}$

By cross multiplication we get,

$7(x + 1) = 6(x + 3)$

$7x + 7 = 6x + 18$

$7x - 6x = 18 - 7$

$x = 11$

$\therefore$ Numerator of new rational number = 11

Denominator of the rational number = 11+6 = 17

$\therefore$Rational Number = $\frac{11}{17}$