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.
(i) A tap can fill a tank in 6 hours. In 1 hour, $\frac{1}{6}$ of the tank is filled.
(ii) 18 hours
$(\mathrm{A}+\mathrm{B})$ 's 1 hour work $=\frac{1}{6}$
A's 1 hour work $=\frac{1}{9}$
B's 1 hour work $=\frac{1}{6}-\frac{1}{9}=\frac{3-2}{18}=\frac{1}{18}$
Thus, B takes 18 hours to finish the work.
(iii) 48 hours
A's 1 hour work $=\frac{1}{16}$
B's 1 hour work $=\frac{1}{24}$
C's 1 hour work $=\frac{1}{\mathrm{x}}$
$(\mathrm{A}+\mathrm{B}+\mathrm{C})$ 's 1 hour work $=\frac{1}{8}$
Therefore, $\frac{1}{\mathrm{x}}=\frac{1}{8}-\frac{1}{16}-\frac{1}{24}=\frac{6-3-2}{48}=\frac{1}{48}$
or, $\mathrm{x}=48$ hours
Thus, $\mathrm{C}$ alone takes 48 hours to complete the wor $\mathrm{k}$.
(iv) The time for completion is the reciprocal of the work done in one day. Therefore, A can complete the whole work in $\frac{20}{3}=6 \frac{2}{3}$ days
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