Two persons A, B can together complete a piece of work in 12 days, B and C together complete the same work in 8 days. If A, B, C work together, then that work can be finished in 6 days. Then the number of days B alone can finish the same work is

Solution

A, B can together complete the work in 12 days

Hence efficiency of (A+B) = $$\left(\frac{100}{12}\right)\%$$ = $$8\frac{1}{3\ }\%$$

B and C together complete the same work in 8 days.

Hence efficiency of (B+C) = $$\left(\frac{100}{8}\right)\%$$ = $$12\frac{1}{2\ }\%$$

A, B, C work together, then that work can be finished in 6 days

Hence efficiency of (A+B+C) = $$\left(\frac{100}{6}\right)\%$$ = $$16\frac{2}{3\ }\%$$

Effeciencies

A+B = $$8\frac{1}{3\ }\%$$         .......(i)     

B+C = $$12\frac{1}{2\ }\%$$        ......(ii)

A+B+C =$$16\frac{2}{3\ }\%$$    .....(iii)

Solving for B, 

iii - ii

(A+B+C) - (B+C) = A= $$16\frac{2}{3\ }\%$$ - $$12\frac{1}{2\ }\%$$ = $$4\frac{1}{6\ }\%\ =\ \frac{25}{6\ }\%$$

Putting this in (i)

$$\ \frac{25}{6\ }\%$$ + B = $$8\frac{1}{3\ }\%$$

B =$$8\frac{1}{3\ }\%$$ -  $$\ \frac{25}{6\ }\%$$ = $$\frac{25}{6\ }\%$$ %

Time taken by B = $$\left(\frac{1}{\ efficicency}\right)$$ = $$\frac{100}{\frac{25}{6\ }}\ =\ 24$$ 

24 days Answer