Question

Tick (✓) the correct answer:
3 men or 5 women can do a work in 12 days. How long will 6 men and 5 women take to do it?
(a) 6 days
(b) 5 days
(c) 4 days
(d) 3 days

Answer 1

(c) 4 days

$$\begin{gathered} \mathrm{Three}\mathrm{men}\mathrm{can}\mathrm{complete}\mathrm{the}\mathrm{work}\mathrm{in}12\mathrm{days}. \\ \mathrm{Thus},\mathrm{one}\mathrm{man}\mathrm{can}\mathrm{complete}\mathrm{the}\mathrm{work}\mathrm{in}36\mathrm{days}. \\ \mathrm{Rate}\mathrm{of}\mathrm{work}\mathrm{done}\mathrm{by}\mathrm{one}\mathrm{man}\mathrm{in}1\mathrm{day}=\frac{1}{36} \\ \mathrm{Similarly},\mathrm{rate}\mathrm{of}\mathrm{work}\mathrm{done}\mathrm{by}\mathrm{one}\mathrm{woman}\mathrm{in}1\mathrm{day}=\frac{1}{5\times 12}=\frac{1}{60} \\ \mathrm{Now},\mathrm{six}\mathrm{men}\mathrm{will}\mathrm{do}\frac{6}{36},\mathrm{i}.\mathrm{e}.,\frac{1}{6}\mathrm{unit}\mathrm{of}\mathrm{work}\mathrm{in}\mathrm{a}\mathrm{day}. \\ \mathrm{Five}\mathrm{women}\mathrm{will}\mathrm{do}\frac{5}{60},\mathrm{i},\mathrm{e}.,\frac{1}{12}\mathrm{unit}\mathrm{of}\mathrm{work}\mathrm{in}\mathrm{a}\mathrm{day}. \\ \therefore \mathrm{Total}\mathrm{work}\mathrm{done}\mathrm{in}1\mathrm{day}=\frac{1}{6}+\frac{1}{12}=\frac{1}{4}\mathrm{unit} \\ \mathrm{Thus},\mathrm{six}\mathrm{men}\mathrm{and}\mathrm{five}\mathrm{women}\mathrm{will}\mathrm{take}4\mathrm{days}\mathrm{to}\mathrm{complete}\mathrm{the}\mathrm{work}. \end{gathered}$$

The work can be completed in 4 days.