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RD Sharma Solutions Class 10 Mathematics Solutions for Real Numbers Exercise 1.2 in Chapter 1 - Real Numbers

Question 12 Real Numbers Exercise 1.2

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 on 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 me how many animals went on each trip?

Answer:

From the question, it’s given that,

Number of goats = 205 Number of donkeys = 140 Number of cows = 175

So, to find the largest number of animals in one trip the HCF (105, 140, and 175) has to be calculated.

Now, first consider the numbers 105 and 140 and apply division lemma 140 = 105 x 1 + 35

105 = 35 x 3 + 0

Thus, the HCF (105 and 140) = 35

Now, consider 35 and the third number 175 and apply Euclid’s division lemma

175 = 35 x 5 +0

Hence, the HCF (105, 140, 175) = 35.

Therefore, it can be said that 35 animals went on in each trip.

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