Question : Rashi can finish work alone in 10 hours, Gopi in 8 hours, and Manju alone in 12 hours. How long will they take if they work together?
Option 1: $3 \frac{11}{37}$ hours
Option 2: $4 \frac{7}{37}$ hours
Option 3: $4 \frac{3}{37}$ hours
Option 4: $3 \frac{9}{37}$ hours
Correct Answer: $3 \frac{9}{37}$ hours
Solution :
One day work of Rashi = $\frac{1}{10}$
One day work of Gopi = $\frac{1}{8}$
One day work of Manju = $\frac{1}{12}$
So, one day work of all the three $=\frac{1}{10} + \frac{1}{8} + \frac{1}{12}
= \frac{12}{120} + \frac{15}{120} + \frac{10}{120} = \frac{37}{120}$
⇒ Time taken by all the three if working together $=\frac{120}{37} = 3 \frac{9}{37}$ hours
Hence, the correct answer is $3\frac{9}{37}$ hours.
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