The value of $$1.\overline{36} +3.\overline{24} + 1.\overline{33}\ is:$$​​

Correct option is D

Given:

Expression :$$1.\overline{36} +3.\overline{24} + 1.\overline{33}\ is:$$​​

Solution:

Let x = 1.3636…..

Then, 100x = 136.363636..

100x - x = 136.3636 -1.3636.. = 135

99x = 135

​$$x= \frac{135}{99}$$​​

Similar, let y = 3.242424..

100y = 324.2424…

100y - y = 324.2424… - 3.2424… = 321

99y = 321

$$y= \frac{321}{99}$$​

100z = 133.333

100z - z = 132

​$$z= \frac{132}{99}$$​​

Now,  

​$$\frac{135}{99} + \frac{321}{99} +\frac{132}{99}$$​​

​$$=\frac{135+321+132}{99}$$​​

​$$=\frac{588}{99} = \bf \frac{196}{33}$$