Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long it will take to fill the tank ?

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 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 D

Explanation:

We can get the answer by subtrating work done by leak in one hour by subtraction of filling for 1 hour without leak and with leak, as

Work done for 1 hour without leak = 1/3
Work done with leak =
$$\begin{aligned} 3\frac{1}{2} = \frac{7}{2} \\ \text{Work done with leak in 1 hr= }\frac{2}{7} \\ \text{Work done by leak in 1 hr }\\ = \frac{1}{3} - \frac{2}{7} = \frac{1}{21} \end{aligned}$$

So tank will be empty by the leak in 21 hours.

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 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.