An article costing Rs. 20 was marked 25% above the cost price. After two successive discounts of the same percentage, the customer now pays Rs. 20.25. What would be the percentage change in profit had the price been increased by the same percentage twice successively instead of reducing it?
Solution
Correct Answer: Option D
Cost price of the article = 20
Selling price = 20.25
So, profit = 20.25 – 20 = 0.25 Rs
Let, the successive discount percentage is x.
The mark price of the article was 25% greater than its cost price.
Mark price = 20 + (25/100) × 20 = 25 Rs.
Price after 1st discount \(= {\rm{}}25{\rm{}}-\frac{{25{\rm{x}}}}{{100}}{\rm{}} = {\rm{}}25\left( {1{\rm{}} - \frac{{\rm{x}}}{{100}}} \right)\)
Price after 2nd discount \(= {\rm{}}25{\left( {1{\rm{}} - \frac{{\rm{x}}}{{100}}} \right)^2}\)
This price = 20.25
\(\begin{array}{l} \Rightarrow 25{\left( {1 - \frac{x}{{100}}} \right)^2} = 20.25\\ \Rightarrow \left( {1-\frac{x}{{100}}} \right) = \frac{{4.5}}{5} = 0.9 \end{array}\)
⇒ x = 10%
Now, the marked price was increased by the same percentage, i.e. 10% successively.
Price after 1st price increase \(= 25 + \left( {\frac{{10}}{{100}}} \right) \times 25 = 27.5\ Rs.\)
Price after 2nd price increase \(= 27.5 + \left( {\frac{{25}}{{100}}} \right) \times 27.5 = 30.25\ Rs.\)
Profit for this price = 30.25 – 20 = 10.25
% Change = (Change in profit/Original profit) × 100
So, % change \(= \left[ {\frac{{10.25-0.25}}{{0.25}}} \right] \times 100\)
= 4000%
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