Question

Suppose you have 1200 to save. You have to save some amount at 10% and the rest at 15%. How much should be saved at each rate to yield 12% on the total amount saved?

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{amount}\mathrm{invested}\mathrm{at}10\%\mathrm{be}\mathrm{Rsx}\mathrm{and}\mathrm{amoun}\mathrm{invested}\mathrm{at}15\%\mathrm{be}\mathrm{Rs}\mathrm{y}. \\ \mathrm{Sum}\mathrm{of}\mathrm{the}\mathrm{amount}\mathrm{invested}=\mathrm{Rs}1200 \\ \mathrm{x}+\mathrm{y}=1200 \\ \Rightarrow \mathrm{y}=1200-\mathrm{x}...\left(1\right) \\ \mathrm{He}\mathrm{get}12\%\mathrm{on}\mathrm{the}\mathrm{total}\mathrm{amount}=1200\mathrm{x}\frac{12}{100}=\mathrm{Rs}144...\left(2\right) \\ \mathrm{Interest}=0.10\mathrm{x}+0.15\mathrm{y}=12\%\mathrm{on}\mathrm{the}\mathrm{total}\mathrm{amount} \\ \Rightarrow 0.10\mathrm{x}+0.15(1200-\mathrm{x})=144\left[\mathrm{using}1\mathrm{and}2\right] \\ \Rightarrow 10\mathrm{x}+15(1200-\mathrm{x})=14400 \\ \Rightarrow 10\mathrm{x}+18000-15\mathrm{x}=14400 \\ \Rightarrow 5\mathrm{x}=3600 \\ \Rightarrow \mathrm{x}=720 \\ \mathrm{So},\mathrm{amount}\mathrm{invested}\mathrm{at}10\%=\mathrm{Rs}720 \\ \mathrm{And}\mathrm{amount}\mathrm{invested}\mathrm{at}15\%=\mathrm{Rs}(1200-720)=\mathrm{Rs}480 \end{gathered}$$
Regards