A father can do a job as fast as his two sons working together. If one son does the job in 3 hours and the other in 6 hours,the number of hours taken by the father,to do the job alone is?Options1234
Question
A father can do a job as fast as his two sons working together. If one son does the job in 3 hours and the other in 6 hours,the number of hours taken by the father,to do the job alone is?Options1234
Solution
To solve this problem, we first need to understand that the rate of work done is inversely proportional to the time taken to complete the work.
- The rate of work done by the first son is 1/3 (job/hour) because he completes the job in 3 hours.
- The rate of work done by the second son is 1/6 (job/hour) because he completes the job in 6 hours.
Since they are working together, we can add their rates of work to get the combined rate of work done by the two sons, which is 1/3 + 1/6 = 1/2 (job/hour).
According to the problem, the father works at the same rate as his two sons combined. Therefore, the father's rate of work is also 1/2 (job/hour).
To find out how long it takes the father to complete the job alone, we take the reciprocal of his rate of work. So, the time taken by the father to do the job alone is 1/(1/2) = 2 hours.
So, the correct option is 2.
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