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TANCET 2008 Solution : Work Time

This aptitude practice question is a Work Time problem solving question. The question appeared in TANCET 2008 and is an easy question. Concept tested: Framing work time equations when two people work together in parallel to complete a task.

Question

A father can do a certain job in x hours. His son takes twice as long to do the job. Working together, they can do the job in 6 hours. How many hours does the father take to do the job?

  1. 9
  2. 18
  3. 12
  4. 20
  5. 16

  Correct Answer      Choice (1). The father takes 9 hours to complete the task.


Explanatory Answer

The father completes the job in x hours.
Son takes twice as long to finish the job. So, the son will take 2x hours to complete the same job.
In an hour, the father will complete \\frac{1}{x}) of the total job.
In an hour, the son will complete \\frac{1}{2x}) of the total job.

So, if the father and son work together, in an hour they will complete \\frac{1}{x}) + \\frac{1}{2x}) of the job.
i.e., in an hour they will complete \\frac{3}{2x}) of the job.
The question states that they complete the entire task in 6 hours if they work together.
i.e., they complete \\frac{1}{6}^{th}) of the task in an hour.

Equating the two information, we get \\frac{3}{2x}) = \\frac{1}{6})
Cross multiplying and solving for x we get 2x = 18 or x = 9.
'x' is the time taken by the father to complete the task. The father takes 9 hours to complete the job.

  The correct answer is Choice (1).

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