## Saturday, 22 October 2011

### Algebra-4

You own a pet store. If you put in one canary per cage, you have one canary too many. If you put in two canaries per cage, you have one cage too many. How many canaries and cages do you have?
(A) five canaries and four cages
(B)four canaries and five cages
(C)three canaries and four cages
(D)four canaries and three cages
(E) none of the above
Solution follows here:

Solution:

Let the number of canaries be ‘x’ and the number of cages be ‘y’.
Given that, If you put in one canary per cage, you have one canary too many:
This means that, one canary is left out when each cage is filled with one.
ð x = y + 1        ---(1)
Also given that, If you put in two canaries per cage, you have one cage too many:
This means that, one cage is left vacant when each cage is filled with two canaries. This means, (y-1) cages are filled with 2 canaries each.
ð x = 2(y-1)      ---(2)
Solving (1) and (2), y+1 = 2(y-1) => y+1 = 2y-2 => y = 3
Substituting y value in (1), x = 3+1 = 4
4-canaries and 3-cages