The value of $$0.\overline{56} +0.\overline{43}+0.\overline{89}$$​ is:

Correct option is C

Given:​

​$$0.\overline{56} +0.\overline{43}+0.\overline{89}$$

Concept Used:​

0.$$\overline {ab}$$ = $$\frac{ab}{99}$$ 

Solution:

Let , x = $$0.\overline{56}$$  ....(1)

Multiply by 100,

100 x = 56$$.\overline{56}$$ ....(2)

Substracting equation 1 from equation 2,

100x - x = 56$$.\overline{56}$$​ - $$0.\overline{56}$$​  

99x = 56

x = $$\frac{56}{99}$$ = $$0.\overline{56}$$ 

Similarly, 

​$$0.\overline{43} = \frac{43}{99} ,$$   $$0.\overline{89}$$ = $$\frac{89}{99}$$​​

=$$\frac{56}{99}+ \frac{43}{99}+\frac{89}{99}$$

=$$\frac{56+43+89}{99}$$ = $$\frac{188}{99}$$

= 1 + $$\frac{89}{99}$$

= 1.$$\overline{89}$$​​