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Question Number 174552 by Tawa11 last updated on 03/Aug/22

Commented by Rasheed.Sindhi last updated on 04/Aug/22

$$\mathrm{n}=12;\mathrm{Please}\mathrm{confirm}\mathrm{the}\mathrm{answer}.$$

Commented by Tawa11 last updated on 04/Aug/22

$$\mathrm{I}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{know}\mathrm{the}\mathrm{answer}\mathrm{sir}.$$$$\mathrm{please}\mathrm{workings}\mathrm{to}\mathrm{follow}.$$

Commented by Tawa11 last updated on 04/Aug/22

$$\mathrm{Someone}\mathrm{said}:24\mathrm{approximately}\mathrm{sir}.$$

Answered by Rasheed.Sindhi last updated on 05/Aug/22

$$\mathrm{AnOther}\mathrm{way}$$$$\mathbf{t}\mathrm{is}\mathrm{only}\mathrm{for}\mathrm{comparison}\mathrm{its}\mathrm{value}$$$${\mathrm{doesn}}^{\prime }\mathrm{t}\mathrm{matter}.$$$$\mathrm{Let}\mathrm{for}\mathrm{convenience}\mathrm{t}=\gcd (46,69)=23$$$$\underset{―}{\mathrm{Number}\mathrm{of}\mathrm{vegitables}\mathrm{per}\mathrm{minute}}$$$$\overline{)\begin{array}{cccc}\mathrm{rad}.& \mathrm{cucum}.& \mathrm{onions}& \mathrm{okra}\\ \frac{46}{23}=2& \frac{46}{23}=2& \frac{69}{23}=3& \frac{69}{23}=3\end{array}}$$$$$$$$\underset{―}{\mathrm{Number}\mathrm{of}\mathrm{minutes}\mathrm{per}\mathrm{vegitable}}$$$$\overline{)\begin{array}{cccc}\mathrm{rad}.& \mathrm{cucum}.& \mathrm{onions}& \mathrm{okra}\\ \frac{23}{46}=\frac{1}{2}& \frac{23}{46}=\frac{1}{2}& \frac{23}{69}=\frac{1}{3}& \frac{23}{69}=\frac{1}{3}\end{array}}$$$$$$$$\underset{―}{\mathrm{First}\mathrm{k}\mathrm{minutes}}$$$$\mathrm{k}/4\mathrm{minutes}\mathrm{for}\mathrm{each}\mathrm{vegitable}$$$$\overline{)\begin{array}{ccccc}& \mathrm{rad}.& \mathrm{cucu}.& \mathrm{onions}& \mathrm{okra}\\ \mathrm{per}\min .& 2& 2& 3& 3\\ \mathrm{in}\frac{\mathrm{k}}{4}\mathrm{mins}& \frac{2\mathrm{k}}{4}=\frac{\mathrm{k}}{2}& \frac{2\mathrm{k}}{4}=\frac{\mathrm{k}}{2}& \frac{3\mathrm{k}}{4}& \frac{3\mathrm{k}}{4}\end{array}}$$$$2\left(\frac{\mathrm{k}}{2}\right)+2\left(\frac{3\mathrm{k}}{4}\right)=\frac{5\mathrm{k}}{2}\mathrm{vegitables}.$$$$\underset{―}{\mathrm{Next}\mathrm{k}\mathrm{minutes}}$$$$\mathrm{n}+\mathrm{n}+\mathrm{n}+\mathrm{n}=4\mathrm{n}\mathrm{vegitables}$$$$\mathrm{time}\mathrm{in}\mathrm{each}\mathrm{vegitable}:$$$$\overline{)\begin{array}{ccccc}& \mathrm{rad}.& \mathrm{cucum}.& \mathrm{onions}& \mathrm{okra}\\ \underset{\mathrm{time}}{\mathrm{per}\mathrm{veg}.}& 1/2& 1/2& 1/3& 1/3\\ \underset{\mathrm{n}\mathrm{vegs}}{\mathrm{time}\mathrm{in}}& \frac{\mathrm{n}}{2}& \frac{\mathrm{n}}{2}& \frac{\mathrm{n}}{3}& \frac{\mathrm{n}}{3}\end{array}}$$$$\mathrm{total}\mathrm{time}:2\left(\frac{\mathrm{n}}{2}\right)+2\left(\frac{\mathrm{n}}{3}\right)=\frac{5\mathrm{n}}{3}=\mathrm{k}$$$$$$$$\underset{―}{\mathrm{In}2\mathrm{k}\mathrm{minutes}}$$$$\mathrm{total}\mathrm{vegitables}:$$$$\frac{5\mathrm{k}}{2}+4\mathrm{n}=98$$$$\frac{5}{2}\cdot \frac{5\mathrm{n}}{3}+4\mathrm{n}=98[\because \mathrm{k}=\frac{5\mathrm{n}}{3}]$$$$\frac{49\mathrm{n}}{6}=98$$$$\mathrm{n}=\frac{98\times 6}{49}=12$$

Commented by Tawa11 last updated on 05/Aug/22

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.\mathrm{I}\mathrm{appreciate}.$$

Answered by Rasheed.Sindhi last updated on 05/Aug/22

$$\underset{―}{\mathrm{Number}\mathrm{of}\mathrm{vegitables}\mathrm{per}\mathrm{minute}}$$$$\overline{)\begin{array}{cccc}\mathrm{rad}.& \mathrm{cucum}.& \mathrm{onions}& \mathrm{okra}\\ 46/\mathrm{t}& 46/\mathrm{t}& 69/\mathrm{t}& 69/\mathrm{t}\end{array}}$$$$$$$$\underset{―}{\mathrm{Number}\mathrm{of}\mathrm{minutes}\mathrm{per}\mathrm{vegitable}}$$$$\overline{)\begin{array}{cccc}\mathrm{rad}.& \mathrm{cucum}.& \mathrm{onions}& \mathrm{okra}\\ \mathrm{t}/46& \mathrm{t}/46& \mathrm{t}/69& \mathrm{t}/69\end{array}}$$$$$$$$\underset{―}{\mathrm{First}\mathrm{k}\mathrm{minutes}}$$$$\mathrm{k}/4\mathrm{minutes}\mathrm{for}\mathrm{each}\mathrm{vegitable}$$$$\overline{)\begin{array}{ccccc}& \mathrm{rad}.& \mathrm{cucu}.& \mathrm{onions}& \mathrm{okra}\\ \mathrm{per}\min .& 46/\mathrm{t}& 46/\mathrm{t}& 69/\mathrm{t}& 69/\mathrm{t}\\ \mathrm{in}\frac{\mathrm{k}}{4}\mathrm{mins}& \frac{46\mathrm{k}}{4\mathrm{t}}& \frac{46\mathrm{k}}{4\mathrm{t}}& \frac{69\mathrm{k}}{4\mathrm{t}}& \frac{69\mathrm{k}}{4\mathrm{t}}\end{array}}$$$$2\left(\frac{46\mathrm{k}}{4\mathrm{t}}\right)+2\left(\frac{69\mathrm{k}}{4\mathrm{t}}\right)\mathrm{vegitables}.$$$$\underset{―}{\mathrm{Next}\mathrm{k}\mathrm{minutes}}$$$$\mathrm{n}+\mathrm{n}+\mathrm{n}+\mathrm{n}=4\mathrm{n}\mathrm{vegitables}$$$$\mathrm{time}\mathrm{in}\mathrm{each}\mathrm{vegitable}:$$$$\overline{)\begin{array}{ccccc}& \mathrm{rad}.& \mathrm{cucum}.& \mathrm{onions}& \mathrm{okra}\\ \underset{\mathrm{time}}{\mathrm{per}\mathrm{veg}.}& \mathrm{t}/46& \mathrm{t}/46& \mathrm{t}/69& \mathrm{t}/69\\ \underset{\mathrm{n}\mathrm{vegs}}{\mathrm{time}\mathrm{in}}& \frac{\mathrm{nt}}{46}& \frac{\mathrm{nt}}{46}& \frac{\mathrm{nt}}{69}& \frac{\mathrm{nt}}{69}\end{array}}$$$$\mathrm{total}\mathrm{time}:2\left(\frac{\mathrm{nt}}{46}\right)+2\left(\frac{\mathrm{nt}}{69}\right)=\mathrm{k}$$$$$$$$\underset{―}{\mathrm{In}2\mathrm{k}\mathrm{minutes}}$$$$\mathrm{total}\mathrm{vegitables}:$$$$2\left(\frac{46\mathrm{k}}{4\mathrm{t}}\right)+2\left(\frac{69\mathrm{k}}{4\mathrm{t}}\right)+4\mathrm{n}=98$$$$\mathrm{k}(\frac{46}{2\mathrm{t}}+\frac{69}{2\mathrm{t}})+4\mathrm{n}=98$$$$\because \mathrm{k}=2\left(\frac{\mathrm{nt}}{46}\right)+2\left(\frac{\mathrm{nt}}{69}\right)\mathrm{from}\mathrm{above}.$$$$\therefore (2\left(\frac{\mathrm{nt}}{46}\right)+2\left(\frac{\mathrm{nt}}{69}\right))(\frac{46}{2\mathrm{t}}+\frac{69}{2\mathrm{t}})+4\mathrm{n}=98$$$$\cancel{\mathrm{t}}(2\left(\frac{\mathrm{n}}{46}\right)+2\left(\frac{\mathrm{n}}{69}\right))\cdot \frac{1}{\cancel{\mathrm{t}}}(\frac{46}{2}+\frac{69}{2})+4\mathrm{n}=98$$$$(\frac{\mathrm{n}}{23}+\frac{2\mathrm{n}}{69})\left(\frac{115}{2}\right)+4\mathrm{n}=98$$$$(\frac{25}{6}+4)\mathrm{n}=98$$$$\frac{49}{6}\mathrm{n}=98$$$$\mathrm{n}=\frac{98\times 6}{49}=12$$

Commented by Tawa11 last updated on 05/Aug/22

$$\mathrm{Wow},\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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