Transporting 105 Goats, 140 Donkeys and 175 Cows Across a River

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

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. The boatman insists that he will take the same number of animals in every trip and they must be of the same kind. He wants to take the largest possible number each time. How many animals went in each trip?

Step 1: Identify the Mathematical Concept

The largest possible number of animals that can be taken in each trip (of the same kind) is the HCF (Highest Common Factor) of 105, 140 and 175.

Step 2: Find the HCF of 105, 140 and 175

105 = 3 × 5 × 7

140 = 2 × 2 × 5 × 7

175 = 5 × 5 × 7

Common factors = 5 × 7

HCF = 35

Final Answer

∴ The largest possible number of animals that went in each trip is 35.

Conclusion

Thus, by using the HCF of 105, 140 and 175, we find that the boatman carried 35 animals of the same kind in each trip.