Question

A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened, What is the total time taken to fill the tank completely ?
1. 4 hrs.
2. 3 hrs. 45 mins.
3. 3 hrs. 15 mins.
4. 4 hrs. 15 mins.

Answer 1

Correct Answer - Option 2 : 3 hrs. 45 mins.

Given:

A Time take by a tap to fill a tank = 6 hours

Work is done by the tap = 1/2

Similar three taps are opened with the same efficiency

Formula Used:

In the LCM method 

Number of days = Total work\efficiency

Calculation:

Lcm for 6 = 6 units

⇒Total work = 6 units

⇒The efficiency of 1^st tap = 1 

⇒Half work is done = 3 units

Time taken by a Tap to fill half tank = 3/1 ⇒ 3hours

Remaining work = 6 - 3 ⇒ 3 units 

3 extra taps with similar efficiency are opened

⇒The total efficiency of all 4 taps = 4

Number of hours to fill = remaining work/Total efficiency of all taps

Time take by all 4 taps = (3/4) × 60⇒ 45 minutes 

∴ The total time taken by all taps to fill a tank = 3 hours and 45 minutes

Alternate method:

A Time take by a tap to fill a tank = 6 hours

Time taken by tap to fill a tank in 1 hour = 1/6

Let us take the Total work to be  1unit

time taken by the tap to fill half tank = 6 × 1/2 ⇒ 3 hours      ----(ii)

Work remaining = 1/2 unit

similar three taps are opened 

Time take to complete the remaining work by the four taps be x

4 × (1/6)x = 1/2  

x = 3/4 hour ⇒ 45 minutes      ----(ii)

Adding (i) and (ii) we get

∴ Total time taken by all taps to fill a tank is 3 hour and 45 minutes