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04 May 2022, 08:15
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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72% (02:56) correct
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To do a certain work B would take three times as long as A and C together and C twice as long as A and B together. The three men complete the work together in 10 days. How long would each take separately?
A. 20, 60, 40
B. 24, 40, 30
C. 10, 90, 20
D. 12, 90, 18
E. 24, 80, 36
Are You Up For the Challenge: 700 Level Questions
A. 20, 60, 40
B. 24, 40, 30
C. 10, 90, 20
D. 12, 90, 18
E. 24, 80, 36
Are You Up For the Challenge: 700 Level Questions
05 May 2022, 11:03
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To save time, I will focus on solving for C only.
It takes C twice as long as A and B together to do a certain work: \(C = 2(A + B)\)
\(\frac{C}{2}= A+B\)
We are also told that the three men complete the work together in 10 days: \(\frac{1}{A}+\frac{1}{B}+\frac{1}{C}=\frac{1}{10}\)
Substituting in A+B = C/2 into the above:
\(\frac{1}{\frac{C}{2}}+\frac{1}{C}=\frac{1}{10}\)
\(\frac{2}{C}+\frac{1}{C}=\frac{1}{10}\)
\(\frac{3}{C}=\frac{1}{10}\)
\(C = 30\)
Answer B
It takes C twice as long as A and B together to do a certain work: \(C = 2(A + B)\)
\(\frac{C}{2}= A+B\)
We are also told that the three men complete the work together in 10 days: \(\frac{1}{A}+\frac{1}{B}+\frac{1}{C}=\frac{1}{10}\)
Substituting in A+B = C/2 into the above:
\(\frac{1}{\frac{C}{2}}+\frac{1}{C}=\frac{1}{10}\)
\(\frac{2}{C}+\frac{1}{C}=\frac{1}{10}\)
\(\frac{3}{C}=\frac{1}{10}\)
\(C = 30\)
Answer B
05 May 2022, 14:58
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Bunuel
B would take three times as long as A and C together.
Time and rate have a reciprocal relationship.
Since the time ratio for B and A+C = 3:1, the rate ratio for B and A+C = 1:3.
Let the job = 40 widgets.
The three men complete the work together in 10 days.
Since A+B+C take 10 days to produce the 40-widget job, the combined rate for A+B+C \(= \frac{work}{time} = \frac{40}{10} = 4\) widgets per day.
Since the rate ratio for B and A+C = 1:3, the rate for B = 1 widget per day, while the rate for A+C = 3 widgets per day, for a combined rate of 4 widgets per day.
B's rate of 1 widget per day implies that B's time to produce the 40-widget job \(= \frac{work}{rate} = \frac{40}{1} = 40\) days.
If we assume that the times in the answer choices are for A, B and C in that order -- something the prompt should make clear -- only one option indicates a time of 40 hours for B.
