Question

A barrel filled with water has various holes at it's bottom. The first hole empties the barrel in three days. The second hole empties it in five days. The third in 20hrs and last in 12hrs. If all holes are open, how much time will it take to empty the barrel ?

Answer 1

Solution:
The 1st hole empties the barrel in = 3 days or 72 hours.
In one hour it empties = 1/72 part 
The 2nd hole empties the barrel in = 5 days = 120 hours.
In one hour it empties = 1/120 part
The 3rd hole empties the barrel in = 20 hours
In one hour it empties = 1/20 part
The 4th hole empties the barrel in = 12 hours
In one hour it empties = 1/12 part
Now, we have add it all.
 
 1/72 + 1/120 + 1/20 + 1/12

 10   +     6     +  36   +   60
______________________
             720

= 112/720 = 7/45 part
All the four holes empty the 7/45 part of the full barrel in one hour.
 Now, to find out the total time taken by all the four holes to empty the barrel , we have to divide 1 by 7/45
1 full barrel ÷ 7/45
= 1 × 45/7 
= 45/7
So, the time taken to empty the full barrel by all the four holes is 45/7 hours or 6 by 3/7 hours.
Answer.