Ana is thrice as efficient as Bill and is, therefore, able to finish a piece of work 10 days earlier than Bill. In how many days Ana and Bill will finish it together.
Solution
Correct Answer: Option C
Assume that the whole work is W units.
Efficiency of Bill = B units/day
Efficiency of Ana = 3B units/day
Time taken by Bill to finish the work alone \(= \;\frac{W}{B}\;days\)
Time taken by Ana to finish the work alone \(= \;\frac{W}{{3B}}\;days\)
According to the question, Ana can finish the work 10 days earlier than Bill.
\(\begin{array}{l} \Rightarrow \frac{W}{B} - \frac{W}{{3B}} = 10\\ \Rightarrow \frac{W}{B} = 15 \end{array}\)
When they work together their combined efficiency is (B + 3B) = 4B units/day
Time required to finish it together \(= \;\frac{W}{{4B}} = \frac{{15}}{4} = 3\frac{3}{4}days\) [Using \(\frac{W}{B} = 15\) days ]
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