# Fill in the blanks.  (i) A tap can fill a tank in 6 hours. The part of the tank filled in 1 hour is……………

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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 3/20, then A can finish the whole work in……… days.

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(i) $\frac{1}{6}$

If A can do a piece of work in n days, then A can do $\frac{1}{n}$ of the work in on day

(ii) 18

Number of hours A required do a piece of work : 9 hours

Let number of hours B required do a piece of work : X hours

Number of hours required by A and B together to do a piece of work : 6 hours

Work done by A in one hour: $\frac{1}{9}$

Work done by B in one hour: $\frac{1}{x}$

Work done by A and B together in a hour: $\frac{1}{6}$

Work done by A and B together in one hour: $\frac{1}{9}+\frac{1}{x}=\frac{x\,+\,9}{9x}=\frac{1}{6}$

∴ $\frac{x\,+\,9}{9x}=\frac{1}{6}$

⇒ 6X +54 = 9X

⇒ 3X = 54

⇒ X = $\frac{54}{3}=18$

∴ B can do the work 18 hours

(iii) 48

Number of hours A required do a piece of work : 16 hours

Number of hours B required do a piece of work : 24 hours

Let number of hours C required to do a piece of work : X hours

Number of hours required by A, B and C together to do a piece of work : 8 hours

Work done by A in one hour: $\frac{1}{16}$

Work done by B in one hour: $\frac{1}{24}$

Work done by C in one hour: $\frac{1}{x}$

Work done by A, B and C together in a one hour : $\frac{1}{8}$

Work done by A, B and C together in one hour : $\frac{1}{16}+\frac{1}{24}+\frac{1}{x}=\frac{5}{48}+\frac{1}{x}$

$\frac{5x\,+\,48}{48x}=\frac{1}{8}$

∴ $\frac{5x\,+\,48}{48x}=\frac{1}{8}$

⇒ 40X +384 = 48X

⇒ 8X = 384

⇒ X = $\frac{384}{8}$ = 48 hours

∴ C can do the work 48 hours.

(iv) $6\frac{2}{3}$

If A can do a piece of work in n days, then A can do $\frac{1}{n}$ of the work in on day

∴ $\frac{20}{3}=6\frac{2}{3}$