Question

Two pipes can fill a tank in 8 hrs and 12 hrs reapectively whereas an escape pipe can empty it in 6 hrs .if the three pipes are opened at 1pm,2pm,3pm respectively,at what time will the tank will be filled.​

Answer 1

Tank position at 3pm is

1/4 +1/12=4/12=1/3 full

To be filled is 2/3

All are open at 3pm

Effective filling per hour is

1/8 +1/12–1/6=(3+2-4)/24=1/24th per hour

Time to fill full is 24 hrs

Time to fill 2/3=24*2/3=16 hrs

Time of filling is next day morning 7 AM

Answer 2

Let us consider the name the pipes are= P, Q and R

Filling efficiency of pipe P = $\frac{1}{8}$ per hr

Filling efficiency of pipe Q = $\frac{1}{12}$ per hr

Emptying efficiency of pipe R = $\frac{1}{6}$ per hr

P and Q pipes if works simultaneously fill 1/8 + 1/12

                                                                      =$12 + 8 / 96$ per hr

                                                                      =$\frac{20}{96}$  tank / hour

Working together the efficiency Et = 1/8+1/12–1/6

                                                         =( 9 + 6 )- 12 / 72

                                                        = 15 - 12 /72

                                                        = $\frac{3}{72}$

                                                         = $\frac{1}{24}$ per hr

If all pipes are allowed to operate the tank will be filled in 24 hrs .

P starts at 1 pm and thus operates one hour more than Q as Q starts at 2pm similarly R operates at 3 pm so Q operates one hour more

∴Part of the tank filled in 2 hrs = 2×1/8

Part of the tank filled in 1 hr = 1/12

Part filled = 1/4 +1/12 = 1/3

Hence left over part = 1 - 1/3 = 2/3

Working together 1/24 part filled in 1 hr

Full part = 24hr

2/3 part = (2/3)×24 = 16 hrs

Hence tank will be filled by 7 AM next day.

Ans :- The tank will be filled by 7 AM next day.