Question

Tick (✓) the correct answer:
A does 20% less work than B. If A can finish a piece of work in $7\frac{1}{2}$ hours, then B can finish it in
(a) 5 hours
(b) $5\frac{1}{2}$ hours
(c) 6 hours
(d) $6\frac{1}{2}$ hours

Answer 1

(c) 6 hours

$$\begin{gathered} \mathrm{Time}\mathrm{taken}\mathrm{by}\mathrm{A}\mathrm{to}\mathrm{finish}\mathrm{the}\mathrm{piece}\mathrm{of}\mathrm{work}=7\frac{1}{2}\mathrm{hours}=\frac{15}{2}\mathrm{hours} \\ \mathrm{Work}\mathrm{done}\mathrm{by}\mathrm{A}\mathrm{in}1\mathrm{hour}=\frac{2}{15} \\ \mathrm{Let}\mathrm{B}\mathrm{take}x\mathrm{hours}\mathrm{to}\mathrm{finish}\mathrm{the}\mathrm{work}. \\ \mathrm{Work}\mathrm{done}\mathrm{by}\mathrm{B}\mathrm{in}1\mathrm{hours}=\frac{1}{x} \\ \mathrm{A}\mathrm{can}\mathrm{work}20\%\hspace{0.17em}\mathrm{less}\mathrm{than}\mathrm{B},\mathrm{or}\mathrm{A}\mathrm{can}\mathrm{do}\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$5$}\right.\mathrm{of}\mathrm{B}\text{'}\mathrm{s}\mathrm{work}. \\ \mathrm{Now},\frac{\left({\displaystyle \frac{4}{5}}\right)}{1}=\frac{\left({\displaystyle \frac{2}{15}}\right)}{\left({\displaystyle \frac{1}{\mathrm{x}}}\right)} \\ \Rightarrow \frac{4}{5}=\frac{2\mathrm{x}}{15} \\ \Rightarrow \mathrm{x}=\frac{15\times 4}{5\times 2}=6\mathrm{hours} \end{gathered}$$