Question : At a construction site, Raju can paint a wall in 36 hours, while Angad can do the same work in 18 hours. Sumit can paint the same wall in 24 hours. In how much time can they paint the wall if they all work together?
Option 1: 9 hours
Option 2: 12 hours
Option 3: 6 hours
Option 4: 8 hours
Correct Answer: 8 hours
Solution :
The rate at which Raju can paint the wall is $\frac{1}{36}$ of the wall per hour.
Similarly, the rates for Angad and Sumit are $\frac{1}{18}$ and $\frac{1}{24}$ of the wall per hour, respectively.
When they all work together, their combined rate is,
$\frac{1}{36} + \frac{1}{18} + \frac{1}{24} = \frac{2+4+3}{72} = \frac{9}{72}= \frac{1}{8}$
Therefore, the time it takes for them to paint the wall together = $\frac{1}{\frac{1}{8}} = 8 $
Hence, the correct answer is 8 hours.
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