# 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.

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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