A tank can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tank from empty state if B is used for the first half time and then A and B fill it together for the other half.

Answer: Option C

Explanation:

Capacity of the tank = (12*13.5) litres
= 162 litres
Capacity of each bucket = 9 litres.
So we can get answer by dividing total capacity of tank by total capacity of bucket.
Number of buckets needed = (162/9) = 18 buckets

Answer: Option D

Explanation:

Part filled by A in 1 hour = 1/5
Part filled by B in 1 hour = 1/10
Part filled by C in 1 hour = 1/30

Part filled by (A+B+C) in 1 hour =
$$\begin{aligned} \frac{1}{5}+\frac{1}{10}+\frac{1}{30} \\ = \frac{1}{3} \\ \end{aligned}$$

So all pipes will fill the tank in 3 hours.

Answer: Option C

Explanation:

Work done by the inlet in 1 hour =
$$\begin{aligned} \frac{1}{6}-\frac{1}{8} = \frac{1}{24} \\ \text{Work done by inlet in 1 min} \\ = \frac{1}{24}*\frac{1}{60}\\ = \frac{1}{1440} \\ => \text{Volume of 1/1440 part = 4 liters} \\ \end{aligned}$$

Volume of whole = (1440 * 4) litres = 5760 litres.

Answer: Option A

Explanation:

Part filled in 3 minutes =
$$\begin{aligned} 3*\left(\frac{1}{12} + \frac{1}{15}\right) \\ = 3*\frac{9}{60} = \frac{9}{20}\\ \text{Remaining part }= 1-\frac{9}{20} \\ = \frac{11}{20} \\ => \frac{1}{15}:\frac{11}{20}=1:X \\ => X = \frac{11}{20}*\frac{15}{1} \\ => X = 8.25 mins \end{aligned}$$

So it will take further 8 mins 15 seconds to fill the bucket.

Answer: Option C

Explanation:

When we have question like one is filling the tank and other is empting it, then we subtraction as,

Filled in 1 hour = 1/4
Empties in 1 hour = 1/9

Net filled in 1 hour = 1/4 - 1/9
= 5/36

So cistern will be filled in 36/5 hours i.e. 7.2 hours