Question

Tick (✓) the correct answer:
A and B together can do a piece of work in 12 days; B and C can do it in 20 days while C and A can do it in 15 days. A, B and C all working together can do it in
(a) 6 days
(b) 9 days
(c) 10 days
(d) $10\frac{1}{2}$ days

Answer 1

(c) 10 days

$$\begin{gathered} (\mathrm{A}+\mathrm{B})\mathrm{can}\mathrm{do}\mathrm{a}\mathrm{work}\mathrm{in}12\mathrm{days}. \\ (\mathrm{B}+\mathrm{C})\mathrm{can}\mathrm{do}\mathrm{a}\mathrm{work}\mathrm{in}20\mathrm{days}. \\ (\mathrm{C}+\mathrm{A})\hspace{0.17em}\mathrm{can}\mathrm{do}\mathrm{a}\mathrm{work}\mathrm{in}15\mathrm{days}. \\ \mathrm{Now},\mathrm{we}\mathrm{have}: \\ \mathrm{Work}\mathrm{done}\mathrm{by}(\mathrm{A}+\mathrm{B})\mathrm{in}1\mathrm{day}=\frac{1}{12} \\ \mathrm{Work}\mathrm{done}\mathrm{by}(\mathrm{B}+\mathrm{C})\mathrm{in}1\mathrm{day}=\frac{1}{20} \\ \mathrm{Work}\mathrm{done}\mathrm{by}(\mathrm{C}+\mathrm{A})\mathrm{in}1\mathrm{day}=\frac{1}{15} \\ \mathrm{Net}\mathrm{work}\mathrm{done}\mathrm{by}2(\mathrm{A}+\mathrm{B}+\mathrm{C})=\frac{1}{12}+\frac{1}{20}+\frac{1}{15}=\frac{5+3+4}{60}=\frac{12}{60}=\frac{1}{5} \\ \mathrm{Net}\mathrm{work}\mathrm{done}\mathrm{by}(\mathrm{A}+\mathrm{B}+\mathrm{C})\mathrm{in}1\mathrm{day}=\frac{1}{10} \\ \therefore \mathrm{If}\mathrm{A},\mathrm{B}\mathrm{and}\mathrm{C}\mathrm{work}\mathrm{together},\mathrm{they}\mathrm{will}\mathrm{complete}\mathrm{the}\mathrm{work}\mathrm{in}10\mathrm{days}. \end{gathered}$$