PC and laptop

A person spent Rs 50000 to purchase a desktop computer and a laptop computer. He sold the desktop at a 20% profit and the laptop at a 10% loss. If, overall, he made a 2% profit, then find the purchase price, in rupees, for the desktop.

Correct answer:

d =  21666.6667

Step-by-step explanation:

$$\begin{gathered} r_1=100\%+20\%=1+\frac{20}{100}=1.2 \\ {r}_2=100\%-10\%=1-\frac{10}{100}=0.9 \\ {r}_3=100\%+3\%=1+\frac{3}{100}=1.03 \\ 50000=d+l \\ 50000\cdot r_3=d\cdot r_1+l\cdot r_2 \\ 50000=d+l \\ 50000\cdot 1.03=d\cdot 1.2+l\cdot 0.9 \\ d+l=50000 \\ 1.2d+0.9l=51500 \\ Pivot:Row1\leftrightarrow Row2 \\ 1.2d+0.9l=51500 \\ d+l=50000 \\ Row2-\frac{1}{1.2}\cdot Row1\to Row2 \\ 1.2d+0.9l=51500 \\ 0.25l=7083.33 \\ l=\frac{7083.33333323}{0.25}=28333.33333326 \\ d=\frac{51500-0.90000000000146l}{1.2}=\frac{51500-0.9\cdot 28333.33333326}{1.2}=21666.66666674=21666.6667 \\ d=\frac{65000}{3}\doteq 21666.666667 \\ l=\frac{85000}{3}\doteq 28333.333333 \end{gathered}$$

Try another example