Question

The ratio of the numerator and denominator of a rational number is 2 : 7 and

if 4 is added to the numerator and 2 is subtracted from denominator, the
rational number becomes 10
19
. Find the original rational number.

Answer 1

6/21.

Explanation:

let the rational number be 2x/7x.

2x + 4 / 7x - 2 = 10 /19

Cross multiply:

19(2x + 4) = 10(7x - 2)

38x + 76 = 70x - 20

96 = 70x - 38x

32x = 96

x = 3.

So the rational number is 2*3/ 7*3

= 6/21.