Question

A can do a piece of work in 10 days while B alone can do it in 15 days. In how many days can both finish the same work?

Answer 1

$$\begin{gathered} \mathrm{A}\mathrm{can}\mathrm{do}\mathrm{a}\mathrm{piece}\mathrm{of}\mathrm{work}\mathrm{in}10\mathrm{days}. \\ \mathrm{A}\text{'}\mathrm{s}1\mathrm{day}\mathrm{work}=\frac{1}{10} \\ \mathrm{B}\mathrm{can}\mathrm{do}\mathrm{a}\mathrm{piece}\mathrm{of}\mathrm{work}\mathrm{in}15\mathrm{days}. \\ \mathrm{B}\text{'}\mathrm{s}1\mathrm{day}\mathrm{work}=\frac{1}{15} \\ (\mathrm{A}+\mathrm{B})\text{'}\mathrm{s}1\mathrm{day}\mathrm{work}=\frac{1}{10}+\frac{1}{15}=\frac{3+2}{30}=\frac{5}{30}=\frac{1}{6} \\ \mathrm{A}\mathrm{and}\mathrm{B}\mathrm{working}\mathrm{together}\mathrm{can}\mathrm{complete}\mathrm{the}\mathrm{work}\mathrm{in}6\mathrm{days}. \end{gathered}$$