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Question 110
If a + $$\ \frac{1}{b}\ $$= 1 and b + $$\frac{1}{c}$$= 1 then c +Â $$\ \frac{1}{a}$$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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