3 friends Amar Akbar and Anthony were about to cross the river and their passenger boats. Amar had more passengers and his boat could not hold, so he requested Akbar to take half of number Akbar's passenger from Amar's boat. Now Akbar's boat lost its balance, he called Anthony and pleased to take half the number of anthonys passengers from Akbar's boat on his own. at the end when all the boats with stable all had equal number of passengers can you guess the total number of passenger in all 3 boards added together?
Answers
Given : Amar requested Akbar to take half of number Akbar's passenger from Amar's boat.
Anthony take half the number of anthonys passengers from Akbar's boat on his own
Finally all had equal number of passengers
To find : total number of passenger in all 3 boards added together
Solution:
Let say Passenger in Amar Boat= X
Passenger in Akbar Boat = Y
Passenger in Anthony Boat = Z
Request Akbar to take half of number Akbar's passenger from Amar's boat
=> Amar Boat passengers = X - Y/2
Passenger in Akbar Boat = Y + Y/2 = 3Y/2
half the number of anthonys passengers from Akbar's boat on
Passenger in Akbar Boat = 3Y/2 - Z/2
Passenger in Anthony Boat = Z + Z/2 = 3Z/2
X - Y/2 = 3Y/2 - Z/2 = 3Z/2
3Y/2 - Z/2 = 3Z/2
=> 3Y - Z = 3Z
=> 3Y = 4Z
X - Y/2 = 3Y/2 - Z/2
=> X = 2Y - Z/2
=> X = 2Y - 3Y/8
=> X = 13Y/8
=> 8X = 13Y
=> 24X = 39Y
3Y = 4Z
=> 39Y = 52Z
=> 24X = 39Y = 52Z
LCM of 24 , 39 & 52 = 312
=> X/13 = Y/8 = Z/6
=> X : Y : Z = 13 : 8 : 6
13 + 8 + 6 = 27 Total passenger in all 3 boards added together
or multiple of 27
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