Question : In an office, typing work can be finished by Monika in 6 hours, Anita in 8 hours, and Manju in 5 hours if they work alone. How much time (in hours) will they take if they work together?
Option 1: $3 \frac{3}{59}$
Option 2: $2 \frac{2}{59}$
Option 3: $2 \frac{2}{5}$
Option 4: $2 \frac{2}{57}$
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Correct Answer: $2 \frac{2}{59}$
Solution :
Work done by Monika in 1 hour = $\frac{1}{6}$
Work done by Anita in 1 hour = $\frac{1}{8}$
Work done by Manju in 1 hour = $\frac{1}{5}$
Work done together in one hour = $\frac{1}{6}$+$\frac{1}{8}$+$\frac{1}{5}$
= $\frac{20+15+24}{120}$ = $\frac{59}{120}$
The typing can be complete together in $\frac{120}{59} = 2\frac{2}{59}$ hours
Hence, the correct answer is $2\frac{2}{59}$.
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