Ques1- Alok worked on a set of mathematics problems for 20 min and finished 4/15 of it. He then called Asha. Working together, they finished the complete set in 22min. How long would Asha and Alok alone had taken to finish the set?

Ques2- Pipe A can fill tank in 3hrs. Pipe B can fill tank in 4hrs. An outlet pipe C can empty the tank in 6hrs. If all three pipes are kept open simultaneously, in how many hrs will the tank will be half full?

Ques3- Tap A fills tank in 2hrs. Outlet B and c can empty the tank in 4hrs and 6hrs respectively. If the tank is empty and A and B are turned on, hoe long will it take to fill up? After the tank A,B and C are all turned on. How long will the tank take to be empty?

Ques4- Tap A can fill a tank in 8min. Outlet B can empty the tank in 12min. If both are kept open,how long will it take to fill the tank?

Answer :

1 ) Remaining task = 1- 415 = 1115

415 task takes time of Alok =20 min

1 task will take time =20 × 154  = 75 min.  (ans)

Both took time to complete 1115 task = 22 min
And Alok alone took time to complete 1115 task = 75 - 20  =  55 min
Let
Asha alone took time to complete 1115 task = x
 
So, we get
155 + 1x = 122x+ 5555x = 12222x+ 1210 = 55x33x =  1210 x =  1210 33x =  110 3
So,
1115 task takes time of Asha  = 1103 min

1 task will take time =1103 × 1511  = 50 min.  ( Ans )



2 ) Total work done to fill the tank by pipe A and B in 1 hr  = 13 +14 = 712

Work done by pipe C to empty the tank in 1 hr  = 16

Work done to fill the tank in 1 hr = 712 -16 = 512

Work done to fill half tank in 1 hr = 512 × 2 = 1210
So,

Time taken to fill the half tank when all thee pipes open =1210 =1.2 hrs                           (ans)

3 ) Work done if A and B are open to fill the tank in 1 hr  =12 - 14= 14

Time taken to fill the tank  = 4 hrs  (ans)

Work done if A, B, and c are open in 1 hr =12 - 14 - 16 = 112

Time taken to empty  the tank = 12hrs  (ans)


4 ) Work done by A and B in 1 hr = 18 - 112 = 124
So,
Time taken to fill the tank = 24min                                                             (ans)

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