108 cows, 120 sheep and 132 goats are to be taken across a river. There is only one boat and the boatman says, he will take the same number and same kind of animals in each trip. Find the largest number of animals in each trip and the number of trips he will have to make.
Answers
SOLUTION
GIVEN
- 108 cows, 120 sheep and 132 goats are to be taken across a river.
- There is only one boat and the boatman says, he will take the same number and same kind of animals in each trip.
TO DETERMINE
The largest number of animals in each trip and the number of trips he will have to make.
EVALUATION
Here it is given that 108 cows, 120 sheep and 132 goats are to be taken across a river.
Now the boatman will take the same number and same kind of animals in each trip.
So the given numbers are 108 , 120 , 132
108 = 2 × 2 × 3 × 3 × 3
120 = 2 × 2 × 2 × 3 × 5
132 = 2 × 2 × 3 × 11
HCF = 2 × 2 × 3 = 12
Hence the largest number of animals in each trip = 12
Number of trips for cows = 108 ÷ 12 = 9
Number of trips for Sheeps = 120 ÷ 12 = 10
Number of trips for goats = 132 ÷ 12 = 11
Hence total number of trips
= 9 + 10 + 11
= 30
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