Question

A can do $\frac{2}{3}$ of a certain work in 16 days and B can do $\frac{1}{4}$ of the same work in 3 days. In how many days can both finish the work, working together?

Answer 1

$$\begin{gathered} \mathrm{A}\mathrm{can}\mathrm{do}\frac{2}{3}\mathrm{work}\mathrm{in}16\mathrm{days} \\ \text{So, w}\mathrm{ork}\mathrm{done}\mathrm{by}\hspace{0.17em}\mathrm{A}\text{\hspace{0.17em}in one}\mathrm{day}=\frac{2}{48}=\frac{1}{24} \\ \mathrm{B}\mathrm{can}\mathrm{do}\frac{1}{4}\mathrm{work}\mathrm{in}3\mathrm{days} \\ \text{So, w}\mathrm{ork}\mathrm{done}\mathrm{by}\mathrm{B}\text{\hspace{0.17em}in one}\mathrm{day}=\frac{1}{12} \\ \mathrm{Work}\mathrm{done}\mathrm{jointly}\mathrm{by}\mathrm{A}\mathrm{and}\mathrm{B}\text{in one}\mathrm{day}=\frac{1}{24}+\frac{1}{12}=\frac{1+2}{24}=\frac{3}{24}=\frac{1}{8} \\ \text{So,}\mathrm{A}\mathrm{and}\mathrm{B}\mathrm{together}\text{will}\mathrm{take}8\mathrm{days}\mathrm{to}\mathrm{complete}\mathrm{the}\mathrm{work}. \end{gathered}$$