A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 litres a minute. When the tank is full, the inlet is opened and due to the leak the tank is empty in 8 hours. The capacity of the tank (in litres) is

Answer: Option B

Explanation:

Net part filled in 1 hour =
$$\begin{aligned} \left(\frac{1}{5}+\frac{1}{6}-\frac{1}{12}\right) \\ = \frac{17}{60} hrs \\ = 3\frac{9}{17} \end{aligned}$$

Answer: Option C

Explanation:

How we can solve this question ?
First we will calculate the work done for 10 mins, then we will get the remaining work, then we will find answer with one tap work, As

Part filled by Tap A in 1 min = 1/20
Part filled by Tap B in 1 min = 1/60

(A+B)'s 10 mins work =
$$\begin{aligned} 10*\left(\frac{1}{20}+\frac{1}{60}\right) \\ = 10*\frac{4}{60} = \frac{2}{3} \\ \text{Remaining work = } 1-\frac{2}{3} \\ = \frac{1}{3} \\ \text{METHOD 1} \\ => \frac{1}{60}:\frac{1}{3}=1:X \\ => X = 20 \\ \text{METHOD 2} \\ 1/60 \text{ part filled by B in} = 1 min \\ 1/3 \text{ part will be filled in} \\ = \frac{\frac{1}{3}}{\frac{1}{60}} \\ = \frac{60}{3} = 20 \end{aligned}$$

Answer: Option A

Explanation:

Let the slower pipe alone fill the tank in x minutes
then faster will fill in x/3 minutes.

Part filled by slower pipe in 1 minute = 1/x
Part filled by faster pipe in 1 minute = 3/x

Part filled by both in 1 minute = $$\begin{aligned} \frac{1}{x} + \frac{3}{x}= \frac{1}{36} \\ => \frac{4}{x} = \frac{1}{36} \\ x = 36*4 = 144 mins \end{aligned}$$

Answer: Option A

Explanation:

Lets suppose tank got filled by first pipe in X hours,
So, second pipe will fill the tank in X + 10 hours.

$$\begin{aligned} => \frac{1}{X} + \frac{1}{X} + 10 = \frac{1}{12} \\ => X = 20 \end{aligned}$$

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.