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

  1. 2
  2. 1
  3. 1/2
  4. 0
Anurag Mishra Professor Asked on 10th December 2015 in Maths.
Add Comment
1 Answer(s)

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. 

Anurag Mishra Professor Answered on 11th December 2015.
Add Comment

Your Answer

By posting your answer, you agree to the privacy policy and terms of service.