Question

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

Answer 1

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