Car repair

John bought a car for a certain sum of money. He spent 10% of the cost to repairs and sold the car for a profit of Rs. 11000. How much did he spend on repairs if he made a profit of 20%?

Correct result:

r =  5000 Rs

Solution:

$$\begin{gathered} q=10\mathrm{\%}={\displaystyle \frac{10}{100}}=0.1 \\ p=20\mathrm{\%}={\displaystyle \frac{20}{100}}=0.2 \\ 11000=p\cdot a \\ 11000=0.2\cdot a \\ 0.2a=11000 \\ a=55000 \\ a=x+q\cdot x \\ 54999.9999998=x+0.1\cdot x \\ 1.1x=55000 \\ x=50000 \\ r=q\cdot x=0.1\cdot 50000=5000\text{ Rs} \end{gathered}$$

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