What 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?

Time taken by one tap to fill half of the the tank = 3 hours Part filled by the four taps in 1 hour

$$\eqalign{ & = {4 \times \frac{1}{6}} = \frac{2}{3} \cr & {\text{Remaining}}\,{\text{part}} = {1 - \frac{1}{2}} = \frac{1}{2} \cr & \therefore \frac{2}{3}:\frac{1}{2}::1:x \cr & \Rightarrow x = {\frac{1}{2} \times 1 \times \frac{3}{2}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{3}{4}\,hrs.\,\,i.e.,\,45\,\operatorname{mins} . \cr & {\text{So,}}\,{\text{total}}\,{\text{time}}\,{\text{taken}} = 3\,hrs.\,45\,mins. \cr} $$

118

Q:

Answer:   B) 3 hrs 45 min

Explanation:

Time taken by one tap to fill half of the tank = 3 hrs.

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

Remaining part =1-12=12

23:12::1:x

=> x = 12*1*32=34

So, total time taken = 3 hrs. 45 mins.

Subject: Pipes and Cistern - Quantitative Aptitude - Arithmetic Ability

Option 2 : 3 hrs. 45 mins.

Free

15 Questions 30 Marks 10 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

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