Question : Reena, Veena, and Vimla can do a work in 4 hours, 8 hours, and 12 hours, respectively. In how much time will they finish the work working together?
Option 1: $\frac{2}{11}$ hours
Option 2: $5\frac{2}{11}$ hours
Option 3: $3\frac{2}{11}$ hours
Option 4: $2\frac{2}{11}$ hours
Correct Answer: $2\frac{2}{11}$ hours
Solution :
Reena, Veena and Vimla can do a work in 4 hours, 8 hours, and 12 hours, respectively.
Reena's 1 hour's work = $\frac{1}{4}$
Veena's 1 hour's work = $\frac{1}{8}$
Vimla's 1 hour's work = $\frac{1}{12}$
$\therefore$ (Reena + Veena + Vimla)'s 1 hour's work = $\frac{1}{4}+\frac{1}{8}+\frac{1}{12}=\frac{11}{24}$
So, they will finish the whole work together in $\frac{24}{11}=2\frac{2}{11}$ hours
Hence, the correct answer is $2\frac{2}{11}$ hours.
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