Question

Fill in the blanks.
(i) A tap can fill a tank in 6 hours. The part of the tank filled in 1 hour is .........
(ii) A and B working together can finish a piece of work in 6 hours while A alone can do it in 9 hours. B alone can do it in ......... hours.
(iii) A can do a work in 16 hours and B alone can do it in 24 hours. If A, B and C working together can finish it in 8 hours, then C alone can finish it in ......... hours.
(iv) If A's one day's work is $\frac{3}{20}$, then A can finish the whole work in ......... days.

Answer 1

(i) A tap can fill a tank in 6 hours. In 1 hour, $\frac{1}{6}$ of the tank is filled.

(ii) 18 hours
$$\begin{gathered} (\mathrm{A}+\mathrm{B})\text{'}\mathrm{s}1\mathrm{hour}\mathrm{work}=\frac{1}{6} \\ \mathrm{A}\text{'}\mathrm{s}1\mathrm{hour}\mathrm{work}=\frac{1}{9} \\ \mathrm{B}\text{'}\mathrm{s}1\mathrm{hour}\mathrm{work}=\frac{1}{6}-\frac{1}{9}=\frac{3-2}{18}=\frac{1}{18} \\ \text{Thus,}\mathrm{B}\mathrm{takes}18\mathrm{hours}\mathrm{to}\mathrm{finish}\mathrm{the}\mathrm{work}. \end{gathered}$$


(iii) 48 hours
$$\begin{gathered} \mathrm{A}\text{'}\mathrm{s}1\mathrm{hour}\mathrm{work}=\frac{1}{16} \\ \mathrm{B}\text{'}\mathrm{s}1\mathrm{hour}\mathrm{work}=\frac{1}{24} \\ \mathrm{C}\text{'}\mathrm{s}1\mathrm{hour}\mathrm{work}=\frac{1}{\mathrm{x}} \\ (\mathrm{A}+\mathrm{B}+\mathrm{C})\text{'}\mathrm{s}1\mathrm{hour}\mathrm{work}=\frac{1}{8} \\ \mathrm{Therefore},\frac{1}{\mathrm{x}}=\frac{1}{8}-\frac{1}{16}-\frac{1}{24}=\frac{6-3-2}{48}=\frac{1}{48} \\ \mathrm{or},\mathrm{x}=48\mathrm{hours} \\ \text{Thus,}\mathrm{C}\text{alone}\mathrm{takes}48\mathrm{hours}\mathrm{to}\mathrm{complete}\mathrm{the}\mathrm{wor}\text{k}. \end{gathered}$$

(iv) The time for completion is the reciprocal of the work done in one day. Therefore, A can complete the whole work in $\frac{20}{3}=6\frac{2}{3}\text{days}$