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 same kind. He will naturally like to take the largest possible number each time .The number of animals went in each trip is _________

• A. $75$
• B. $35$
• C. $154$
• D. $63$

Answer 1

Answer: (B)

$35$

To find the largest possible number of animals ,we will find the H.C.F of 105,140 and 175.
$105=3\times 5\times 7$
$140=2\times 2\times 5\times 7$
$175=5\times 5\times 7$
HCF of 105,140 and 175=$5\times 7=35$
Hence The number of animals went in each trip is 35