**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:**

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

**Answer (D)**

thank you

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