Question

Six times the denominator of a fraction is two less
than eight times the numerator and ten times the
numerator equals 20 less than ten times the
denominator. The reciprocal of the fraction is
(A) 6/7
(B) 3/8 (C) 7/9
(D) 917​

Answer 1

Step-by-step explanation:

hence c is the correct option

Answer 2

Answer:

(d) $\frac{9}{7}$

Step-by-step explanation:

Let n represent the numerator and d represent the denominator

Given : Six times the denominator of a fraction is two less than eight times the numerator

=>   6d = 8n-2 ----- (i)

ten times the numerator equals 20 less than ten times the denominator.

=>  10n = 10d-20

=> n = d-2  --------(ii)

putting the value of n in (i) equation

=> 6d = 8 (d-2) - 2

=> 6d = 8d - 16 - 2

=> 6d = 8d - 18

=> 18 = 8d - 6d

=> 18 = 2d

=> d =$\frac{18}{2}$

=> d = 9

putting the value of d in (ii) equation

=> n = 9-2

=> n = 7

d = 9  and n = 7

$= \frac{7}{9}$

reciprocal   $= \frac{9}{7}$