Question

1.express each of these relationships as a rate in it's simplest form.
1.1. 12kg for R5.
1.2. 120 litres for 1000km.
1.3. R355 for two nights.
1.4. 7km in 28 min.
1.5. 145 students for five teachers.

Answer 1

$(1)\\ 12 \hspace{0.1cm}\textsf{kg for} \hspace{0.1cm} R5 \\ \begin{aligned} \textsf{Since}\hspace{0.1cm} 1\hspace{0.1cm}\textsf{kg} &=1000g\\ 1R &= 100\hspace{0.1cm} \textsf{paise}\\ \end{aligned}\\ \begin{aligned} \therefore 12\hspace{0.1cm}\textsf{R}5 &= 12000g \hspace{0.1cm}\textsf{per}\hspace{0.1cm} 500\hspace{0.1cm} \textsf{paise} \\&= 24 \hspace{0.1cm}\textsf{g/paise} \end{aligned}\\ (2)\\ \begin{aligned} 120\hspace{0.1cm} \textsf{litres per}\hspace{0.1cm} 1000\hspace{0.1cm}\textsf{km} &= \frac{120}{1000} \hspace{0.1cm} \textsf{litres/km} \\&= 0.12 \hspace{0.1cm} \textsf{litres/km} \end{aligned}\\ (3)\\ \begin{aligned} R355 \hspace{0.1cm} \textsf{per} \hspace{0.1cm}2 \hspace{0.1cm}\textsf{nights} &= \frac{355}{2}\hspace{0.1cm} \textsf{R/nights} \\&= 177.5\hspace{0.1cm} \textsf{R/nights} \end{aligned}\\ (4)\\ \begin{aligned}7\hspace{0.1cm}\textsf{km}\hspace{0.1cm} \textsf{in} \hspace{0.1cm}28\hspace{0.1cm} \textsf{min} \hspace{0.1cm}\textsf{nights} &= \frac{7\times 1000}{28}\hspace{0.1cm} \textsf{m/min} \\&= 250\hspace{0.1cm} \textsf{m/min} \end{aligned}\\ (5)\\ \displaystyle 145 \hspace{0.1cm} \textsf{students for just five teachers} \\= \frac{145}{5}\hspace{0.1cm} \textsf{students/teacher} \\=29\hspace{0.1cm} \textsf{students/teacher}$