Question 13

A is four times efficient as B. B started the work and after 6 days, A joined him. If the whole work was completed in 12 days, in how many days A alone can finish the whole piece of work ?

Solution

Let work = 1 units

Let time taken by A to complete the work = $$x$$ days

=> Time taken by B = $$4x$$ days

Acc to ques,

=> $$\frac{12}{4x} + \frac{6}{x} = 1$$

=> $$\frac{6}{x} (\frac{1}{2} + 1) = 1$$

=> $$\frac{3}{2} = \frac{x}{6}$$

=> $$x = \frac{3}{2} \times 6$$

=> $$x = 9$$ days

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