Discussion
Which of the following is/are correct?
1. A and B together can do a piece of work in 12 days. B and C together can do it in 15 days. If A is twice as good a workman as C, then B alone can finish the work in 20 days.
2. If Ram can do a piece of work in 10 days and Shyam can complete the same work in 6 days, then both of them together complete the work within 4 days.
Select the answer using the code given below:
Answer: C
Both 1 and 2 are correct.
Statement 1: write the daily work rates as a, b, c with a = 2c.
\[ \begin{aligned} a + b &= \tfrac{1}{12},\ \ b + c = \tfrac{1}{15} \\ (a + b) - (b + c) &= c = \tfrac{1}{12} - \tfrac{1}{15} = \tfrac{1}{60} \\ b &= \tfrac{1}{15} - \tfrac{1}{60} = \tfrac{1}{20} \end{aligned} \]
Here a − c = c because a = 2c. So B alone takes 20 days. True.
Statement 2: together Ram and Shyam do \(\tfrac{1}{10} + \tfrac{1}{6} = \tfrac{8}{30}\) a day, so they take \(30/8 = 3.75\) days, which is within 4 days. True.
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