Question

in a tank there are three pipes.we can fill the tank from 1st 2pipes in 3hours and 3hours 45 minutes.whearasvthe third pipe empty the tank in one hour.if all the three pipes is opened in 1 pm ,2pm and 3 pm respectively then when did the tank get empty.​

Answer 1

Answer:

10.00 p.m

Step-by-step explanation:

let A,B,and C be the pipes

given ,

Time taken by pipe A to fill the tank = 3 hours

Time taken by pipe B to fill the tank = 2 hours

Time taken by pipe c to empty the tank = 1 hour

capacity of the Tank

l.c.m of 3,2,1 = 6

so the Capacity of the Tank is 6 liters

efficiency of the pipes

efficiency of pipe A = 6/3 = 2 liters/hour

efficiency of pipe B = 6/2 = 3 liters/hour

efficiency of pipe C = 6/-1 =  -6 liters/hour

=> efficiency of pipes A & B together = 2+3 = 5 liters/hour

and efficiency of pipes A,B,and C = 2+3-6 = -1 litre/hour

part of Tank filled

pipe A is opened at 1 pm to  2pm (given)

ie, pipe A opened for 1 hour

part of tank filled at 2pm = 1 hour x 2 liters/hour = 2 litres

then

pipes A & B are opened together from 2pm to 3pm

ie, both pipes A&B are running for 1 hour

so, part of tank filled at that 1 hour = 1 hour x 5 litres/hour = 5 litres

and we have part of tank filled at 3pm =  2 litres + 5 litres = 7 litres

pipes A,B,C are opened at 3pm

as the efficiency of A,B&C are negative, only draining of tank only will be happening from 3pm onwards.

so let us calculate the time taken to drain the 7 litres filled so far.

so time taken to drain the tank = 7 litres / -1 litre/hour = 7 hours

ie, when A,B,and C are running from 3pm, it takes 7 hours to empty the tank

=> 3.00 pm +7 hours = 10.00 p.m

the tank will be empty by 10.00 p.m