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Work done by A in one day is half of the work done by B in one day. Work done by B is half of the work done by C in one day. If C alone can complete the work in 7 days, in how many days can A, B and C together complete the work ?

Work done by A in one day is half of the work done by B in one day. Work done by B is half of the work done by C in one day. If C alone can complete the work in 7 days, in how many days can A, B and C together complete the work ? Correct Answer 4 days

$$\eqalign{ & {\text{C's 1 day's work}} \cr & = \frac{1}{7} \cr & {\text{B's 1 day's work}} \cr & = \left( {\frac{1}{2} \times \frac{1}{7}} \right) \cr & = \frac{1}{{14}} \cr & {\text{A's 1 day's work}} \cr & = \left( {\frac{1}{2} \times \frac{1}{{14}}} \right) \cr & = \frac{1}{{28}} \cr & \left( {{\text{A}} + {\text{B}} + {\text{C}}} \right){\text{'s 1 day's work}} \cr & = \left( {\frac{1}{{28}} + \frac{1}{{14}} + \frac{1}{7}} \right) \cr & = \frac{7}{{28}} \cr} $$
Hence, A, B and C together can complete the work in 4 days.

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