Question

105 goats, 140 donkeys and 175 cows have to be taken across a river. There is only one boat which will have to make many trips in order to do so. The lazy boatman has his own conditions for transporting them. He insists that he will take the same number of animals in every trip and they have to be of the same kind. He will naturally like to take the largest possible number each time. Can you tell how many animals went in each trip?

Answer 1

Number of goats = 205

Number of donkey = 140

Number of cows = 175

∴ The largest number of animals in one trip = HCF of 105, 140 and 175

First consider 105 and 140

By applying Euclid’s division lemma

140 = 105 × 1 + 35

105 = 35 × 3 + 0

∴ HCF of 105 and 140 = 35

Now consider 35 and 175

By applying Euclid’s division lemma

175 = 35 × 5 + 0

HCF of 105, 140 and 175 = 35