M43-04

Question

On Monday, a pipe working continuously filled an empty tank at an average (arithmetic mean) rate of 75 liters per hour. The next day, the pipe began filling another empty tank of the same volume. However, during this process, it was turned off for some time due to maintenance, resulting in a longer filling time. This reduced its average filling rate to 60 liters per hour. How many minutes per hour was the pipe turned off on Tuesday?

A. 10
B. 12
C. 15
D. 20
E. 25

Show Answer

Official Answer

B

A. 10
B. 12
C. 15
D. 20
E. 25

Bunuel · Answer

Official Solution:

On Monday, a pipe working continuously filled an empty tank at an average (arithmetic mean) rate of 75 liters per hour. The next day, the pipe began filling another empty tank of the same volume. However, during this process, it was turned off for some time due to maintenance, resulting in a longer filling time. This reduced its average filling rate to 60 liters per hour. How many minutes per hour was the pipe turned off on Tuesday?

A. 10
B. 12
C. 15
D. 20
E. 25

Show Answer

Official Answer

B

A. 10
B. 12
C. 15
D. 20
E. 25

There are many ways to solve this question; however, arguably the least error-prone method is to assume a specific volume for the tank. Let's say its volume is 300 liters (the least common multiple of 75 and 60). This would mean that without the maintenance interruption, the pipe would take  \frac{300}{75} = 4  hours to fill the tank. With the maintenance interruption, it would take  \frac{300}{60} = 5  hours. Thus, the pipe was turned off for 1 hour out of 5, which makes 1/5 of an hour per hour, or 12 minutes per hour.

Answer: B

Rebaz · Answer

Bunuel

Does  On Monday, a pipe working continuously  mean that the pipe worked during the whole 24 hours throughout Monday? If yes, then it seems we easily can get the volume of the tank by multiplying 75 liters per hour by 24 hours = 1800 liter is the tank capacity?

Is my approach regarding the tank capacity correct?

Thanks in advance!

Bunuel · Answer

This does not mean that the pipe worked for all 24 hours on Monday. It simply means that during the time the pipe was in operation on Monday, it worked continuously without any interruptions.

saibharatmba · Answer

Hi Rebaz,

It doesn't matter. You can take it as 24 hours as well. Answer won't change. This is a ratio and proportion problem. What proportion of an hour was tap idle?

75min for 1 hour --> 5 parts
60min for 1 hour --> 4 parts

remaining 1 part is idle time which is 1/5*60min = 12min

Jayant9090 · Answer

hi,
 Bunuel 
what went wrong in my approach?

Since volume is same in both days, we can have below equation-
75*t=60*(t+x)
which on solving gives x=t/4
i.e. 60*1/4=15 mins/hr.

Bunuel · Answer

If solving it that way, you should take the ratio of x to t + x, which represents the total time. This gives x/(t + x) = 1/5.

Prateek_Sood · Answer

I think this is a  high-quality  question.

vishwaraje · Answer

I like the solution - it’s helpful.

M43-04

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