Question : Riya alone can complete a piece of work in 6 days while Siya alone can do the same work in 9 days. If they both work together, then how many days will be required to finish the work?
Option 1: $\frac{45}{13}$
Option 2: $\frac{18}{5}$
Option 3: $\frac{33}{17}$
Option 4: $\frac{55}{16}$
Correct Answer: $\frac{18}{5}$
Solution :
Given: Riya alone can complete a piece of work in 6 days while Siya alone can do the same work in 9 days.
Let the total work = LCM of 6 and 9 = 54 units
So, the efficiency of Riya = $\frac{54}{6}$ = 9,
and the efficiency of Siya = $\frac{54}{9}$ = 6
Total efficiency = (9 + 6) = 15
So, together they will finish the work in $\frac{54}{15}$ = $\frac{18}{5}$ days
Hence, the correct answer is $\frac{18}{5}$.
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