BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Three pipes - A, B, and C - are attached to a tank. Pipe A

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2505
Joined: Sun Oct 15, 2017 1:50 pm
Followed by:6 members

Three pipes - A, B, and C - are attached to a tank. Pipe A

by BTGmoderatorLU » Tue Oct 02, 2018 2:58 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Source: e-GMAT

Three pipes - A, B, and C - are attached to a tank. Pipe A alone can fill the empty tank in 6 hours, pipe B alone can empty the full tank in 8 hours and pipe C alone can fill the empty tank in 12 hours. At 9 am pipe A is opened. One hour after that pipe B is opened and one hour from that pipe C is opened. At what time the tank will be full?

A. 11:40 am
B. 12:27 pm
C. 1:40 pm
D. 5 pm
E. 5:20 pm

The OA is E.
Top
Source: — Problem Solving |
Junior | Next Rank: 30 Posts
Posts: 25
Joined: Mon May 07, 2018 8:47 am
Location: India
GMAT Score:610

Edited the solution.

by nonplus2 » Tue Oct 02, 2018 5:28 pm
Given:

Pipe A alone can fill the tank in 6 hours
Pipe B alone can empty the tank in 8 hours
Pipe C alone can fill the tank in 12 hours

Next crucial step, is to check whether the Total Work is defined with a specific Quantity. If not then to establish the given relations in the questions we can assume the work to be a VERY EASY TO WORK NUMBER.

EASY to Work number in most cases, for such question types, is usually the LCM of given rates.

In this case the LCM of rates (6,8,12) is 24. However, personally i would not use 24 as the Total capacity of the tank, i would rather choose 120(which is a multiple of 24) for ease of calculations.

Multiples of 10 are easier to work & they put me at ease. Imagine trying to solve this question under exam pressure, won't you welcome any possible comfort in the calculations? I definitely would.

Back to the question,

Assuming Total capacity of the Tank as 120 litres.

Pipe A alone can fill the Tank in 6 hours, hence rate of filling of A = 120/6 = 20 litres/hour

Pipe B alone can empty the Tank in 8 hours, hence rate of emptying of B = 120/8 = 15 litres/hour

Pipe C alone can fill the Tank in 12 hours, hence of rate of filling of C = 120/12 = 10 litres/hour

Now,

Activity 1
Pipe A is opened at 9 am, for one hour, till 10 am.

Pipe A alone for one hour will fill the Tank with 20 litres

Hence the Tank still has 120-20 = 100 litres left to be filled.

Activity 2
Pipe B is opened at 10 am, for one hour, till 11 am.

Pipe A filling the Tank & Pipe B Emptying the Tank for one hour.

Hence, 20 litres filled in & 15 litres emptied out in one hour, has a resultant effect of (20 - 15) = 5 litres filled in.

That means the Tank still has 100 - 5 = 95 litres to be filled in

Activity 3
Pipe C is opened at 11 am, now all pipes are open till the Tank is full. The three pipes together have to give a net effect of filling 95 litres.

Pipe A, B & C working together for one hour will have a resultant effect of (20-15+10) = 15 litres filled in one hour.

Hence in 6 hours, together they will fill 90 litres.

The remaining 5 litres will take (5*60)/15 = 20 mins, since all pipes together fill 15 litres per 60 mins

Therefore with all the pipes opened, the tank will fill the remaining 95 litres in 6 hours & 20 mins.

Now Total Time Taken to fill the Tank = 1 Hour (Pipe A) + 1 Hour (Pipe A+Pipe B) + 6 Hours 20 mins (Pipe A + Pipe B + Pipe C) = 8 hours 20 mins

Therefore the Time at which the Tank will be full is 9 am + 8 hours 20 mins = 5:20 pm.

Answer E. $$$$ $$$$
Last edited by nonplus2 on Tue Oct 02, 2018 10:50 pm, edited 1 time in total.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Tue Oct 02, 2018 10:28 pm
BTGmoderatorLU wrote:Source: e-GMAT

Three pipes - A, B, and C - are attached to a tank. Pipe A alone can fill the empty tank in 6 hours, pipe B alone can empty the full tank in 8 hours and pipe C alone can fill the empty tank in 12 hours. At 9 am pipe A is opened. One hour after that pipe B is opened and one hour from that pipe C is opened. At what time the tank will be full?

A. 11:40 am
B. 12:27 pm
C. 1:40 pm
D. 5 pm
E. 5:20 pm

The OA is E.
The rates of the pipes are:

1. Pipe A: 1/6 part per hour (It fills)
2. Pipe B: -1/8 part per hour (It empties)
2. Pipe C: 1/12 part per hour (It fills)

1. Between 9 to 10 am: Part of the tank filled by pipe A = 1/6
2. By 11 am: Part of the tank filled by pipe A and empties by pipe B = 2*(1/6) - 1/8 = 5/24

Part of the tank remaining to be filled = 1 - 5/24 = 19/24

By 11 am onwards, all the three pipes are open.

Part of the tank filled by pipe A & C and emptied by pipe B in one hour = 1/6 - 1/8 + 1/12 = 1/8

Thus, the time required to fill 19/24 part = (19/24) / (1/8) = 19/3 hours = 6 hours 20 minutes

Total time = 2 + 6 : 20 = 8 hours 20 minutes => The tank will fill by 5:20 pm.

The correct answer: E

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Jakarta | Nanjing | Berlin | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top
Post new topic Post Reply
• Page 1 of 1