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Amit, Bhawana and Chandan can do a piece of work, working together in one day only. Amit is 5 times efficient than Bhawna and Chandan takes half of the number of days taken by Bhawna to do the same work. What is the difference between the number of days taken by Amit and Chandan when they work alone ?

Amit, Bhawana and Chandan can do a piece of work, working together in one day only. Amit is 5 times efficient than Bhawna and Chandan takes half of the number of days taken by Bhawna to do the same work. What is the difference between the number of days taken by Amit and Chandan when they work alone ? Correct Answer $${\text{2}}\frac{2}{5}$$

  Amit     Bhawana     Chandan
Eff. →   5x x 2x

$$\eqalign{ & {\text{Let total work}} = 1 \cr & {\text{Efficiency of }}\left( {{\text{A}} + {\text{B}} + {\text{C}}} \right) = 1 \cr & {\text{Then,}} \cr & \Leftrightarrow 5x + x + 2x = 1 \cr & \Leftrightarrow x = \frac{1}{8} \cr & {\text{Days taken by Amit}} \cr & = \frac{1}{{\frac{5}{8}}} \Rightarrow \frac{8}{5} \cr & {\text{Days taken by Chandan}} \cr & = \frac{1}{{\frac{2}{8}}} \Rightarrow 4 \cr & {\text{Difference of days}} \cr & = 4 - \frac{8}{5} \Rightarrow \frac{{20 - 8}}{5} \Rightarrow 2\frac{2}{5} \cr} $$

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