A alone can finish a piece of work in 42 days. B is 20% more efficient than A and C is 40% more efficient than B. In how many days B and C working together can finish the same piece of work? (in days)

Let rate at which A finishes the work = $$100x$$ units/day

=> Rate at which B finishes the work = $$\frac{120}{100} \times 100x = 120x$$ units/day

Rate at which C finishes the work = $$\frac{140}{100} \times 120x = 168x$$ units/day

Work done by A in 42 days = $$42 \times 100x = 4200x$$ units/day

Rate at which B and C finishes the work = $$120x + 168x = 288x$$ units/day

$$\therefore$$ Time taken by B and C together to finish the same work = $$\frac{4200x}{288x}$$

= $$\frac{175}{12} = 14\frac{7}{12}$$ days