Fill in the blanks.
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.

Solution:

(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