Question

The cost of manufacturing an item is partly fixed and partly depending on the number of items produced. If the cost of manufacturing 35 items is Rs 295 and that of producing 20 items if Rs 175,find the fixed cost and that of producing one item.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{fixed}\mathrm{cost}=\mathrm{Rs}x \\ \mathrm{Let}\mathrm{the}\mathrm{cost}\mathrm{of}\mathrm{producing}1\mathrm{item}=\mathrm{Rs}y \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{the}\mathrm{given}\mathrm{conditions}: \\ x+35y=295......\left(1\right) \\ x+20y=175......\left(2\right) \\ \mathrm{subtracting}\left(2\right)\mathrm{from}\left(1\right),\mathrm{we}\mathrm{get} \\ 35y-20y=295-175 \\ \Rightarrow 15y=120 \\ \Rightarrow y=8 \\ \mathrm{Now},\mathrm{from}\left(1\right),\mathrm{we}\mathrm{get} \\ x+280=295 \\ \Rightarrow x=15 \\ \mathrm{So},\mathrm{fixed}\mathrm{cost}=\mathrm{Rs}15 \\ \mathrm{cost}\mathrm{of}\mathrm{producing}\mathrm{one}\mathrm{item}=\mathrm{Rs}8 \end{gathered}$$