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1. If $\frac{4}{9}$ th of a bucket is filled in 1 minute, the rest of it will be filled in ?

A. $1 minute$

B. $\frac{9}{4} minute$

C. $\frac{5}{4} minute$

D. $\frac{4}{5} minute$

Solution:

Remaining part

\begin{aligned} = (1 - \frac{4}{9}) \\ = \frac{5}{9} \end{aligned}

Let the required time be x minutes
More volume to be filled , More time taken (Direct proportion)

\begin{aligned} ∴ \frac{4}{9} : \frac{5}{9} :: 1 : x \\ \Rightarrow \frac{4}{9} x = \frac{5}{9} \\ \Rightarrow x = (\frac{5}{9} \times \frac{9}{4}) \\ \Rightarrow x = \frac{5}{4} \end{aligned}

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