Solution:

The part of the tank filled by A and B in first two hour

⇒ 3/4×(1/5+1/10)+(1/5+1/10)

The part of tank filled by C in first two hours =2×2/3×1/15

Remaining part =139/360

In 1 hour, all the three pipes together will fill =11/30

Hence, the time taken to fill the remaining tank =139/360×30/11=1.0530 hour.

Thus, the total time taken to fill the remaining tank = 3.05 hour.

Solution:

As per the information given, the ratio of efficiencies of Dr. Gupta, Dr. Sharma and Dr. Singh are 42:30:25

Hence, the ratio of time taken by Dr. Gupta and Dr. Sharma =5:7

Dr. Gupta takes 10 days less than Dr. Sharma, time taken by them will be 25 days and 35 days respectively.

Hence, time taken by Dr. Singh will be 42 days.<br>Part of work completed by Dr. Gupta =2/5

Part of work completed by Dr. Sharma =3/7

Remaining work =1−(2/5+3/7)=6/35

 will be completed by Dr. Singh

He can complete it in 42×6/35

= 7.2 days.

Let the capacity of the tank be C.
Rate of Pipe A = C/A  
Rate of Pipe B = C/B  
Rate of Pipe A and Pipe B together = C/A + C/B = C/8  

 C/12 + C/B   = C/8  
C/B   = C/8 – C/12 = C/24  
Pipe B independently will take 24 hours to fill the tank.