Three fill pipes A, B and C can fill separately a cistern in 3,4
and 6 minutes respectively. A was opened first. After 1
minute, B was opened and after 2 minutes from the start of
A, C was also opened. Find the time when the cistern will be
- full ?
(b) 45 min
(a) 2-min
9
3
(c) 3-min
4
(d) None of these
Answers
Answer:
d is the answer
Step-by-step explanation:
A, B and C can fill separately a cistern in 3,4
and 6 minutes
Let's find out the capacity of tank
Take the LCM of their being time
LCM = 12 means 12 is the total capacity of tank
Let's find out the efficiency of A, B and C of 1 min
A efficiency = 12/3 = 4
B efficiency = 12/4 = 3
C efficiency = 12/6 = 2
Rate/Efficiency * Time = Capacity
Only A fill the tank for first minute
=> 4 * 1 = 4 capacity
Now A and B fill the tank for second minute
=> (A+B) * 1
=> (4 + 3)*1 = 7 Capacity
Means total 11 capacity has been filled in 2 min
Remaining capacity = 12 - 11 = 1 capacity
Remaining Capacity is filled by A,B and C
=> 1/(A + B + B)
=> 1/(4 + 3 + 2)
=> 1/9
1/9min time taken by A, B and C to fill the remaining capacity
Total Time Taken = 1 + 1 + 1/9 = 2 + 1/9 = 19/9 min