Question

the denomenator of a rational number is greater than its numarater by 8 if the denominator is decreased by 1 and numarater increased by 17 ,the number obtainedis 3/2 find rational number

Answer 1

ANSWER:-

Given:

The denominator of a rational number is greater than its numerator by 8 if the denominator is decreased by 1 & numerator increased by 17, the number obrained is 3/2.

To find:

The rational number.

Solution:

Let the numerator of rational number is R & the denominator of rational number is M.

Therefore,

Denominator, M= R+8

The rational number is;

$\frac{R}{M} = \frac{R}{R + 8}$

According to the question:

$\frac{R + 17}{R + 8 - 1} = \frac{3}{2} \\ \\ = > \frac{R + 17}{r + 7} = \frac{3}{2} \\ [Cross \: multiplication]\\ = > 2R + 34 = 3R + 21 \\ \\ = > 2R - 3R = 21 - 34 \\ \\ = > - R = - 13 \\ \\ = > R= 13$

So,

Denominator, M= R +8

=) 13 + 8

=) 21

Therefore,

The rational number is 13/21.

Hope it helps ☺️