Question 58

A is 50% more efficient than B and C is 40% less efficient than B. Working together, they can complete a task in 10 days. In how many days will A alone complete 150% of that task?

Solution

Efficiency of B = $$\frac{1}{x}$$

Efficiency of A = $$\frac{1.5}{x}$$

Efficiency of C = $$\frac{0.6}{x}$$

Total efficiency = $$\frac{1}{x}$$ + $$\frac{1.5}{x}$$ + $$\frac{0.6}{x}$$

=  $$\frac{1}{x}$$ (1+ $$\frac{3}{2}$$ + $$\frac{3}{5}$$)= $$\frac{31}{10x}$$ = $$\frac{1}{10}$$

x= 31

A's efficiency = $$\frac{1.5}{31}$$

150% of that task will be completed in $$\frac{150}{100}$$ / $$\frac{15}{310}$$ = 31 days

So the answer would be option a)31 days.


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