Question

in a bottle making factory 1 mission takes 2 hours to fill 123 bottles then how much time will it take to fill 500 bottles?

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{are}\mathrm{given}\mathrm{that},\mathrm{in}\mathrm{a}\mathrm{factory}\mathrm{a}\mathrm{machine}\mathrm{takes}2\mathrm{hours}\mathrm{to}\mathrm{fill}123\mathrm{bottles}. \\ \mathrm{Let}\mathrm{the}\mathrm{time}\mathrm{taken}\mathrm{by}\mathrm{the}\mathrm{machine}\mathrm{to}\mathrm{fill}500\mathrm{bottles}=\mathrm{t}\mathrm{hours} \end{gathered}$$

In tabular form,

Number of bottles filled	2	x
time taken (in hours)	123	500

$$\begin{gathered} \mathrm{Since}\mathrm{time}\mathrm{taken}\mathrm{and}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{bottles}\mathrm{filled}\mathrm{varies}\mathrm{directly},\mathrm{then} \\ \frac{2}{123}=\frac{x}{500} \\ \Rightarrow 123x=1000 \\ \Rightarrow x=\frac{1000}{123}=8\frac{16}{123} \\ \mathrm{So},\mathrm{time}\mathrm{taken}\mathrm{to}\mathrm{fill}500\mathrm{bottles}=8\frac{16}{123}\mathrm{hours} \end{gathered}$$