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:

(A+B)'s 2 hour's work when opened =

$$\begin{aligned} \frac{1}{6}+\frac{1}{4} = \frac{5}{12} \\ (A+B)'s \text{ 4 hour's work} = \frac{5}{12}*2 \\ = \frac{5}{6} \text{Remaining work = } 1-\frac{5}{6} \\ = \frac{1}{6} \\ \text{Now, its A turn in 5 th hour} \\ \frac{1}{6} \text{ work will be done by A in 1 hour}\\ \text{Total time = }4+1 = 5 hours \end{aligned}$$

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 A

Explanation:

There are two important points to learn in this type of question,
First, if both will open then tank will be empty first.

Second most important thing is,
If we are calculating filling of tank then we will subtract as (filling-empting)

If we are calculating empting of thank then we will subtract as (empting-filling)

So lets come on the question now,

Part to emptied 2/5

Part emptied in 1 minute =

$$\begin{aligned} \frac{1}{6} - \frac{1}{10} \\ = \frac{1}{15} \\ => \frac{1}{15}:\frac{2}{5}::1:x \\ => \frac{2}{5}*15 = 6 mins \end{aligned}$$

Answer: Option D

Explanation:

Half tank will be filled in 3 hours
Lets calculate remaining half,

Part filled by the four taps in 1 hour = 4*(1/6) = 2/3

Remaining part after 1/2 filled = 1-1/2 = 1/2

$$\begin{aligned} \frac{2}{3}:\frac{1}{2}::1:X \\ => X = \left( \frac{1}{2}*1*{3}{2} \right) \\ => X = \frac{3}{4} hrs = 45 \text{ mins} \\ \end{aligned}$$
Total time = 3 hours + 45 mins = 3 hours 45 mins

Answer: Option B

Explanation:

In this type of questions we first get the filling in 1 minute for both pipes then we will add them to get the result, as

Part filled by A in 1 min = 1/20
Part filled by B in 1 min = 1/30

Part filled by (A+B) in 1 min = 1/20 + 1/30
= 1/12

So both pipes can fill the tank in 12 mins.