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CaptainLevi
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Deconstructing the Question

A shopkeeper gives a discount of \(20\%\) on the marked price and still makes a profit of \(25\%\).

We need to find the discount required to make only \(10\%\) profit.

Step-by-step

Assume the cost price

\(CP=100\)

A profit of \(25\%\) means the selling price is

\(125\)

This selling price results after a \(20\%\) discount on the marked price.

\(SP=0.8MP\)

\(125=0.8MP\)

\(MP=\frac{125}{0.8}=156.25\)

Now for a profit of \(10\%\), the selling price must be

\(110\)

So

\(110=MP(1-d)\)

Substitute the marked price

\(110=156.25(1-d)\)

\(1-d=\frac{110}{156.25}=0.704\)

\(d=0.296\)

\(29.6\%\)

Answer C
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P%=(M-D-MD/100)% using successive percentage formula
so 25=M-20-20M/100
4M/5=45 OR M=225/4%
and 10=225/4-D-225D/400
25D/16=(225-40)/4
D=185*4/25=29.6%
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