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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: $\frac{55}{16}$


Team Careers360 12th Jan, 2024
Answer (1)
Team Careers360 21st Jan, 2024

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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