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 1st 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