If $$0.72\overline{45} =\frac{a}{b}$$​, where the HCF of a and b is 1, then what is the value of (b-a)?

Correct option is A

Given:

​$$0.72\overline{45}$$​​

Solution:

Let x = 0.72454545…

100x=72.4545…

10000x= 7245.4545..

10000x-100x = 7245.4545..-72.4545..

9900x =7173

​$$x=\frac{7173}{9900}=\frac{797}{1100}$$​​

Hence$$\frac{a}{b} = \frac{797}{1100}$$​

Here 797 and 1100 are co-primes

Hence (b-a) = 1100-797 = 303