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Question Number 33479 by mondodotto@gmail.com last updated on 17/Apr/18

$$\mathbf{A}\mathbf{man}\mathbf{takes}15\mathbf{days}\mathbf{to}$$$$\mathbf{dig}6\mathbf{hectres}.\mathbf{how}\mathbf{long}\mathbf{would}$$$$10\mathbf{boys}\mathbf{take}\mathbf{to}\mathbf{dig}81\mathbf{hectres}$$$$\mathbf{if}2\mathbf{boys}\mathbf{do}\mathbf{the}\mathbf{same}\mathbf{amount}\mathbf{of}$$$$\mathbf{work}\mathbf{as}\mathbf{one}\mathbf{man}?$$

Commented by MJS last updated on 17/Apr/18

$$1\mathrm{man}15\mathrm{days}6\mathrm{hectres}$$$$1\mathrm{man}\frac{15}{6}=\frac{5}{2}\mathrm{days}1\mathrm{hectre}$$$$1\mathrm{man}81\times \frac{5}{2}=\frac{405}{2}\mathrm{days}81\mathrm{hectres}$$$$1\mathrm{boy}2\times \frac{405}{2}=405\mathrm{days}81\mathrm{hectres}$$$$10\mathrm{boys}\frac{405}{10}=40.5\mathrm{days}81\mathrm{hectres}$$$$\mathrm{what}\mathrm{we}\mathrm{have}\mathrm{done}:$$$$\left(\left(\left(15/6\right)\times 81\right)\times 2\right)/10=\frac{15\times 81\times 2}{6\times 10}$$

Commented by mondodotto@gmail.com last updated on 17/Apr/18

$$\mathrm{still}\mathrm{i}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{understand}\mathrm{this}$$

Answered by Rasheed.Sindhi last updated on 17/Apr/18

$$10\mathrm{boys}=5\mathrm{men}$$$$\left(\begin{array}{ccc}\mathrm{men}& \mathrm{days}& \mathrm{hectres}\\ 1& 15& 6\\ 5& \mathrm{x}& 81\\ \left(\mathrm{inverse}\right)& & \left(\mathrm{direct}\right)\end{array}\right)$$$$\mathrm{x}:15::\{\begin{array}{l}1:5\\ 81:6\end{array}$$$$\mathrm{x}\times 5\times 6=15\times 1\times 81$$$$\mathrm{x}=\frac{15\times 1\times 81}{5\times 6}=40\frac{1}{2}\mathrm{days}$$

Commented by mondodotto@gmail.com last updated on 17/Apr/18

$$\mathrm{inverse}\mathrm{\&}\mathrm{direct}\mathrm{what}\mathrm{you}\mathrm{mean}\mathrm{sir}?$$

Commented by Rasheed.Sindhi last updated on 17/Apr/18

$$\mathrm{Inverse}\mathrm{proportion}\mathrm{\&}\mathrm{direct}\mathrm{proportion}.$$

Answered by ajfour last updated on 17/Apr/18

$$2boys\to 6hectares\to 15days$$$$2boys\to 81hectares\to \frac{15}{6}\times 81days$$$$=\frac{15\times 27}{2}=\frac{405}{2}=202\frac{1}{2}days$$$$10boys\to 81hectares\to \frac{405}{2}\times \frac{2}{10}$$$$=40\frac{1}{2}days.$$

Commented by mondodotto@gmail.com last updated on 17/Apr/18

$$\mathrm{thanx}\mathrm{be}\mathrm{blessed}$$

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