After allowing a discount of 20% on the marked price of a lamp, a trader loses 10%.
Question:

After allowing a discount of 20% on the marked price of a lamp, a trader loses 10%. By what percentage is the marked price above the cost price?

Solution:

Let the $\mathrm{CP}$ of the lamp be Rs. 100 .

Loss $=10 \%$ of $\mathrm{CP}=$ Rs. 10

So, SP $=\mathrm{CP}-$ Loss $=$ Rs. $100-$ Rs. $10=$ Rs. 90

The trader allows a discount of $20 \%$.

This means that when the MP is Rs. 100, the SP will be Rs. $80 .$

Now,

If Rs. 80 is the SP, th $e \mathrm{MP}=$ Rs. 100

If Re. 1 is the SP, the M.P $=$ Rs. $\frac{100}{80}$

If $R s .90$ is the SP, the MP $=$ Rs. $\left(\frac{100}{80} \times 90\right)=$ Rs. $112.50$

Hence, the trader mark $s$ his good $s$ at $12.5 \%$ above the cost price.

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