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21 Nov 2024, 09:10
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
88% (01:56) correct
13%
(02:21)
wrong
based on 8
sessions
History
Date
Time
Result
Not Attempted Yet
Three pipes, A, B, and C, are used to fill a tank. Pipe A can fill the tank in 5 hours, Pipe B in 10 hours, and Pipe C in 15 hours. If all three pipes are opened together, but Pipe A is turned off after 2 hours, how much total time will it take to completely fill the tank?(Approx)
A. 3 hours
B. 3.5 hours
C. 4 hours
D. 4.5 hours
E. 5 hours
A. 3 hours
B. 3.5 hours
C. 4 hours
D. 4.5 hours
E. 5 hours
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21 Nov 2024, 09:31
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Quant can have multiple approaches, Idea of this question is to tackle the problem from different prism.
Typical solution:
1. **Calculate each pipe’s rate of filling the tank:**
- Pipe A's rate: \( \frac{1}{5} \) of the tank per hour.
- Pipe B's rate: \( \frac{1}{10} \) of the tank per hour.
- Pipe C's rate: \( \frac{1}{15} \) of the tank per hour.
2. **Calculate the combined rate when all pipes are open:**
- Combined rate = \( \frac{1}{5} + \frac{1}{10} + \frac{1}{15} \).
- Convert to a common denominator (30):
\[
\frac{1}{5} = \frac{6}{30}, \quad \frac{1}{10} = \frac{3}{30}, \quad \frac{1}{15} = \frac{2}{30}
\]
- Adding these:
\[
\frac{6}{30} + \frac{3}{30} + \frac{2}{30} = \frac{11}{30} \text{ of the tank per hour.}
\]
3. **Calculate the amount of the tank filled in 2 hours:**
- In 2 hours, all three pipes together fill:
\[
2 \times \frac{11}{30} = \frac{22}{30} = \frac{11}{15} \text{ of the tank.}
\]
4. **Determine the remaining portion of the tank:**
- The remaining portion = \( 1 - \frac{11}{15} = \frac{4}{15} \) of the tank.
5. **Calculate the combined rate of Pipes B and C (after A is turned off):**
- Combined rate of B and C = \( \frac{1}{10} + \frac{1}{15} \).
- Convert to a common denominator (30):
\[
\frac{1}{10} = \frac{3}{30}, \quad \frac{1}{15} = \frac{2}{30}
\]
- Adding these:
\[
\frac{3}{30} + \frac{2}{30} = \frac{5}{30} = \frac{1}{6} \text{ of the tank per hour.}
\]
6. **Calculate the time needed to fill the remaining \( \frac{4}{15} \) of the tank with Pipes B and C:**
- Time = \( \frac{\text{Remaining portion}}{\text{Rate of B and C}} = \frac{\frac{4}{15}}{\frac{1}{6}} = \frac{4}{15} \times 6 = \frac{24}{15} = \frac{8}{5} = 1.6 \text{ hours.} \)
7. **Calculate the total time to fill the tank:**
- Total time = 2 hours (with all pipes) + 1.6 hours (with Pipes B and C) = \( 2 + 1.6 = 3.6 \) hours.
**Answer:** The correct answer is **B. 3.5 hours.**
Better solution :
Consider the entire work to of 30 parts. (We came to this number by LCM {5,10,15})
So A can do 6 parts work in 1 hr. Hence it take 5 hrs to completed the work.
Similarly B can do 3 parts, C can do 2 parts.
So when they work together for 2 hrss. (6+3+2)*2 => 22 parts is done in 2 hrs.
Hence left out work is 30-22 => parts.
8/(3+2) = 1.6hrs.
So total time to fill the bucket 2+1.6 =>3.6hrs.
Typical solution:
1. **Calculate each pipe’s rate of filling the tank:**
- Pipe A's rate: \( \frac{1}{5} \) of the tank per hour.
- Pipe B's rate: \( \frac{1}{10} \) of the tank per hour.
- Pipe C's rate: \( \frac{1}{15} \) of the tank per hour.
2. **Calculate the combined rate when all pipes are open:**
- Combined rate = \( \frac{1}{5} + \frac{1}{10} + \frac{1}{15} \).
- Convert to a common denominator (30):
\[
\frac{1}{5} = \frac{6}{30}, \quad \frac{1}{10} = \frac{3}{30}, \quad \frac{1}{15} = \frac{2}{30}
\]
- Adding these:
\[
\frac{6}{30} + \frac{3}{30} + \frac{2}{30} = \frac{11}{30} \text{ of the tank per hour.}
\]
3. **Calculate the amount of the tank filled in 2 hours:**
- In 2 hours, all three pipes together fill:
\[
2 \times \frac{11}{30} = \frac{22}{30} = \frac{11}{15} \text{ of the tank.}
\]
4. **Determine the remaining portion of the tank:**
- The remaining portion = \( 1 - \frac{11}{15} = \frac{4}{15} \) of the tank.
5. **Calculate the combined rate of Pipes B and C (after A is turned off):**
- Combined rate of B and C = \( \frac{1}{10} + \frac{1}{15} \).
- Convert to a common denominator (30):
\[
\frac{1}{10} = \frac{3}{30}, \quad \frac{1}{15} = \frac{2}{30}
\]
- Adding these:
\[
\frac{3}{30} + \frac{2}{30} = \frac{5}{30} = \frac{1}{6} \text{ of the tank per hour.}
\]
6. **Calculate the time needed to fill the remaining \( \frac{4}{15} \) of the tank with Pipes B and C:**
- Time = \( \frac{\text{Remaining portion}}{\text{Rate of B and C}} = \frac{\frac{4}{15}}{\frac{1}{6}} = \frac{4}{15} \times 6 = \frac{24}{15} = \frac{8}{5} = 1.6 \text{ hours.} \)
7. **Calculate the total time to fill the tank:**
- Total time = 2 hours (with all pipes) + 1.6 hours (with Pipes B and C) = \( 2 + 1.6 = 3.6 \) hours.
**Answer:** The correct answer is **B. 3.5 hours.**
Better solution :
Consider the entire work to of 30 parts. (We came to this number by LCM {5,10,15})
So A can do 6 parts work in 1 hr. Hence it take 5 hrs to completed the work.
Similarly B can do 3 parts, C can do 2 parts.
So when they work together for 2 hrss. (6+3+2)*2 => 22 parts is done in 2 hrs.
Hence left out work is 30-22 => parts.
8/(3+2) = 1.6hrs.
So total time to fill the bucket 2+1.6 =>3.6hrs.
21 Nov 2024, 09:47
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HarshaBujji
Please fix the formatting of the post. Thank you.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
