​$$[0 . \overline{07} \times 7 . \overline{5}]=\space?$$​​

Correct option is D

Given:

$$[0 . \overline{07} \times 7 . \overline{5}]=\space?$$

Solution

Let x = $$0.\overline{07}$$​​

Multiply both sides by 100 (since two digits repeat):

​$$100x = 7.\overline{07}$$​​

Now subtracting

​$$100x - x = 7.\overline{07} - 0.\overline{07}$$​​

99x = 7

​$$x = \frac{7}{99}$$​​

Similarly

For, y = $$7.\overline{5}$$​​

​$$y = \frac{68}{9}$$​​

Now,

​$$x \times y = \frac{7}{99} \times \frac{68}{9}$$​​

​$$= \frac{7 \times 68}{99 \times 9} = \frac{476}{891}$$​​

Alternate Solution:

$$0.\overline{0a} = \frac{a}{99}$$ 

So, 

​= $$\frac{7}{99}\times \frac{75 - 7}{9}$$​​

= $$\frac{7}{99}\times \frac{68}{9}$$  

= $$\frac{476}{891}$$​​

Thus, the correct option is (d).