Question:medium

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

Updated On: Jan 13, 2026
  • Statement (1) alone is sufficient to answer the question
  • Statement (2) alone is sufficient to answer the question
  • Both the statements together are needed to answer the question
  • Either statement (1) alone or statement (2) alone is sufficient to answer the question
  • Neither statement (1) nor statement (2) suffices to answer the question
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The Correct Option is A

Solution and Explanation

The correct answer is option (A):
Statement (1) alone is sufficient to answer the question

Here's the breakdown of why statement (1) alone is sufficient to answer the question:

The problem describes a work rate scenario. We are given information about a father and his two sons. The father's work rate is related to the combined work rate of his two sons. We want to find how long the father takes to complete the job.

Let's denote:

* Father's work rate as F
* Son 1's work rate as S1
* Son 2's work rate as S2

The problem gives us the core relationship: "A father can do the job twice as fast as his two sons put together." This translates to:

F = 2 * (S1 + S2) or equivalently, 1/F = (1/2) * (1/(S1+S2)) (in terms of time taken)

We're also told that one son (let's say S1) can do the job in 12 hours. So:

S1 = 1/12 (This represents the fraction of work Son 1 completes in 1 hour).

Now, let's analyze each statement:

Statement 1: "The other son can do the job in 6 hours"

* This means S2 = 1/6 (Son 2 completes 1/6 of the job per hour).

* With statement 1, we can calculate the combined work rate of the sons: S1 + S2 = 1/12 + 1/6 = 1/12 + 2/12 = 3/12 = 1/4.

* This means the two sons together can complete the job in 4 hours.

* Since the father is twice as fast, the father can do the job in 4/2 = 2 hours.
* Therefore, Statement 1 alone provides enough information to solve the problem and determine the father's work time.

Statement 2: "The ratio between the number of hours taken by two sons to complete the work is 1 : 2"

* Let the time Son 1 takes be x and the time Son 2 takes be 2x. We know one son (S1) takes 12 hours.
* If we assume S1 is the son taking 12 hours, then 2x = 12, so x = 6. This implies the other son takes 6 hours.
* The fact that Son 1 takes 12 hours (given) and the ratio gives us the exact amount of time, is very useful.
* But without more information, we can only infer the other son is 6 hours, which allows us to find the combined work rate of the two sons.

Since we are given that one son takes 12 hours, and knowing the ratio of time taken to complete the job (1:2), means the other son's time taken can be found. Therefore, knowing that one son can do the job in 12 hours, we can infer that the other son's time is 6 hours and can be used to solve the problem.

Conclusion:

Statement 1 alone gives us the exact time the second son takes. This combined with the initial information that the first son takes 12 hours is enough information to find the time the father takes. Therefore, statement 1 alone is sufficient. Statement 2, while giving us information to help, still requires knowledge from outside of statement 2 to solve.
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