Question

A father can do the job twice as fast as his two sons put together. If one son can do it in 12 hours, in how many hours can the father do the job
Statement 1: The other son can do the job in 6 hours
Statement 2: The ratio between the number of hours taken by two sons to complete the work is 1 : 2

• A. Statement (1) alone is sufficient to answer the question
• B. Statement (2) alone is sufficient to answer the question
• C. Both the statements together are needed to answer the question
• D. Either statement (1) alone or statement (2) alone is sufficient to answer the question
• E. Neither statement (1) nor statement (2) suffices to answer the question

Answer 1

The Correct Option is A

To solve this problem, let's denote the work done by the people involved and determine the time taken by the father to complete the job.

Let's assume the total work is to be completed in a unit, say one job. 

1. According to the problem, one son can complete the job in 12 hours. Therefore, his work rate is \(\frac{1}{12}\) of the job per hour.
2. Statement 1 indicates that the other son can complete the job in 6 hours. Therefore, his work rate is \(\frac{1}{6}\) of the job per hour.
3. Combined, the two sons have a work rate of:

\(\frac{1}{12} + \frac{1}{6} = \frac{1}{12} + \frac{2}{12} = \frac{3}{12} = \frac{1}{4}\) of the job per hour.

1. According to the problem, the father can complete the job twice as fast as the two sons together. Thus, the father's work rate is:

\(2 \times \frac{1}{4} = \frac{1}{2}\) of the job per hour.

1. If the father completes \(\frac{1}{2}\) of the job in an hour, he will take 2 hours to complete the entire job:

\(\text{Time taken by father} = \frac{1}{\frac{1}{2}} = 2 \text{ hours}\)

Based on this calculation, we see that Statement 1 alone is sufficient to determine the time taken by the father to complete the job.

Let's analyze Statement 2:

1. Statement 2 provides the ratio of the time taken by the two sons to complete the work, which is 1:2. This corresponds to the given times in Statement 1 (6 hours and 12 hours respectively), hence no new information is added to determine the father's rate or time.
2. Thus, Statement 2 alone does not provide sufficient details to find out the time taken by the father, as it implicitly reiterates the data given in Statement 1.

Therefore, the correct answer is that Statement (1) alone is sufficient to answer the question.