# 105 goats, 140 donkeys and 175 cows have to be taken across a river.

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?

Solution:

We are given that, 105 goats, 140 donkeys and 175 cows. There is only one boat which will have to make many y 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. We need to tell the number of animals that went in each trip.

Given that

Number of goats = 105

Number of donkeys = 140

Number of cows = 175.

Therefore, the largest number of animals in 1 trip = H.C.F. of 105, 140 and 175.

First we consider 105 and 140.

By applying Euclid’s division lemma

$140=105 \times 1+35$

$105=35 \times 3+0$

Therefore, H.C.F. of 105 and 140 = 35

Now, we consider 35 and 175.

By applying Euclid’s division lemma

$175=35 \times 5+0$

Therefore, H.C.F. of 105, 140 and 175 = 35

Hence, the number of animals went in each trip is 35