There are twice as many chickens as there are dogs and there are twice as many spiders as chickens. There are 680 legs..

Question

There are twice as many chickens as there are dogs and there are twice as many spiders as chickens.
If altogether there are 680 legs then how many dogs are there?

Answer 1

Given ratio is
Spiders : Chicken : dogs : : 4 : 2 : 1
Ratio of thier corresponding legs
4*8 : 2*2 : 1*4
=32 : 4 : 4
=8 : 1 : 1
Now to find contribution of legs from the spiders, chickens and dogs.
8x + x + x = 10x = 680
x = 68
Therefore the contribution of leg count from the three are as follows
68*8 : 68 : 68
Since we need the ratio of the count of heads and not the legs dividing the ratio appropriately with the number of legs each have

68*8/8 : 68/2 : 68/4
= 68 : 34 : 17
ie., Spiders = 68, Chickens = 34 & Dogs = 17.