Question

If x varies directly as y and inversely as z and if x = 8 when y = 5 and z = 3 then find y when x = 12 and z = 4.

Answer 1

$$\begin{gathered} Given: \\ x\alpha y...\left(\mathrm{i}\right) \\ A\mathrm{nd}, \\ x\alpha \frac{1}{z}...\left(\mathrm{ii}\right) \\ \mathrm{From}\left(\mathrm{i}\right)\&\left(\mathrm{ii}\right),weget: \\ x\alpha \frac{y}{z} \\ Or, \\ x=k\times \frac{y}{z}\left(k\mathrm{is}a\mathrm{constant}.\right) \\ \mathrm{When}x=8,y=5\mathrm{and}z=3: \\ 8=\frac{k\times 5}{3} \\ \Rightarrow k=\frac{8\times 3}{5} \\ \Rightarrow k=\frac{24}{5} \\ E\mathrm{quation}\mathrm{of}\mathrm{variation}: \\ x=\frac{24}{5}\times \frac{y}{z} \\ \mathrm{When}x=12\mathrm{and}z=4: \\ 12=\frac{24\times y}{5\times 4} \\ \Rightarrow y=\frac{12\times 20}{24} \\ \Rightarrow y=10 \end{gathered}$$