Question 110

If a + $$\ \frac{1}{b}\ $$= 1 and b + $$\frac{1}{c}$$= 1 then c + $$\ \frac{1}{a}$$is equal to

Solution

Given : $$a+\frac{1}{b}=1$$

=> $$\frac{1}{b}=1-a$$

=> $$b=\frac{1}{(1-a)}$$ -----------(i)

Also, $$b+\frac{1}{c}=1$$

Substituting value from equation (i) in above equation,

=> $$\frac{1}{1-a}=1-\frac{1}{c}$$

=> $$\frac{1}{1-a}=\frac{c-1}{c}$$

=> $$c=c-1-ac+a$$

=> $$ac+1=a$$

=> $$\frac{ac}{a}+\frac{1}{a}=1$$

=> $$c+\frac{1}{a}=1$$

=> Ans - (A)

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