Question

The denominator of a rational number greater than its numerator by 8 if numerator is increased by 17and denominatior is decreased by 1 the number obtained is 3/2 the rational number is?

Answer 1

Let the rational no be x / y

y = x + 8

-x + y = 8 eq1

(x + 17) / (y - 1) = 3 / 2

2 (x + 17) = 3 (y - 1)

2x + 34 = 3y - 3

2x - 3y = -37 eq2

Multiply eq 1 by 2 we get

-2x + 2y = 16
2x -3y = -37

- y = -21

y = 21

Put y in eq. 2

2x - 3×21 = -37

2x = -37 + 63

x = 26

Rational no is = x/y = 21/26


Thanks

Answer 2

Answer:

.

$\underline{\bigstar\:\textsf{According to the given Question :}}$

If the numerator is increased by 17 and denominotar is decreased by 1 the number obtained is 3/2

$:\implies\sf \dfrac{n + 17 }{(n + 8) - 1} = \dfrac{3}{2}\\\\\\:\implies\sf \dfrac{n + 17 }{n + 7} = \dfrac{3}{2}\\\\\\:\implies\sf 2 (n + 17 ) = 3 (n + 7 )\\\\\\:\implies\sf 2n + 34 = 3n + 21\\\\\\:\implies\sf 34-21=3n-2n\\\\\\:\implies\sf n=13$

⠀

$\dag\:\underline{\boxed{\sf Original\:Fraction=\dfrac{n}{n + 8} = \dfrac{13}{(13 + 8)} = \dfrac{13}{21} }}$