# If a+(1/b)=1 and b+(1/c)=1 then c+(1/a) is equal to:

**Answer: (2) 1 **

**Explanation:-**a + 1/b = 1

=>(a b + 1)/b = 1

a b + 1 = b

b – a b = 1

b (1 – a) = 1

b = 1/(1 – a) ………………………… (1)

b + 1/c = 1

From equation (1), b = 1/(1 – a)

1/(1 – a) + 1/c = 1

(c + 1 – a)/c (1 – a) = 1

c – a + 1 = c – c a

– a + 1 = – c a

a – c a = 1

a (1 – c) = 1

a = 1/(1 – c)

Now, the value of c + 1/a

Put the value of a = 1/(1 – c)

Then, c + 1/{1/(1 – c) }

= c + 1 – c

= 1

Thus, the value of c + 1/a = 1

Hence, the answer is (2) 1.