A tap can fill a cistern in 8 hours. After half the tank is full, four more identical taps of the same type are opened. What is the total time taken to fill the tank completely?

Correct option is B

Given:
One tap can fill the cistern in 8 hours.
After half of the tank is filled, 4 more identical taps are opened, making a total of 5 taps.

Concept Used:

The rate of work of each person is the reciprocal of the time they take to complete the work. example,
A complete work in x day,
Rate of work in one day = $$\frac{1}{x}$$​ day

Solution:

One tap fills the entire cistern in 8 hours.
So, the rate of filling per hour = $$\frac{1}{8}$$​ of the tank.

Since only one tap is opened initially, the time taken to fill half of the tank and T for tank:

​$$\frac{1}{8} \times T = \frac{1}{2}$$

T = 4 hours

So, in 4 hours, half of the tank is filled.​​

After 4 hours, four more taps are opened, making a total of 5 taps.
Each tap fills $$\frac{1}{8}$$​ per hour, so five taps together fill:

= $$\frac{5}{8}$$​ of the tank per hour

Time required to fill the remaining half:

​$$\frac{5}{8} \times T = \frac{1}{2}$$

$$T = \frac{1}{2} \times \frac{8}{5} = \frac{4}{5}$$

In minutes:

T = $$\frac{4}{5} \times 60 = 48$$ minutes.

So, the total time taken to fill the tank completely is 4 hours + 48 minutes = 4 hours 48 minutes.

Thus, the correct answer is (b).

Alternative Method:

A filled in 8 hr → Efficiency 1 → Total tank 8L

Half tank filled = 4L

5 p taps open = $$\frac{4}{5}$$ hr

Time = $$\frac{4}{5} \times 60 = 48$$ minutes

Total time = 4 hours 48 minutes

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