Shopkeeper's Percentage Gain or Loss with Price Increase and Successive
Discounts
Scenario:
Every year before the festive season, a shopkeeper increases the price of
products by 35%, then gives two successive discounts of 10% and 15%. What is
the overall percentage gain or loss? Step-by-Step Calculation: Let the
original cost price (CP) be 100.
- Increase Price by 35%:
- New Marked Price (MP) = 100+35% of 100=135100+35%\text{ of }100=135100+35% of 100=135
- First Discount of 10%:
- Price after first discount = 135−10% of 135=135−13.5=121.5135-10%\text{ of }135=135-13.5=121.5135−10% of 135=135−13.5=121.5
- Second Discount of 15%:
- Price after second discount = 121.5−15% of 121.5=121.5−18.225=103.275121.5-15%\text{ of }121.5=121.5-18.225=103.275121.5−15% of 121.5=121.5−18.225=103.275
- Compare Final Selling Price (SP) with Cost Price (CP):
- Final SP = 103.275
- CP = 100
- Calculate Percentage Gain:
Percentage Gain=SP−CPCP×100=103.275−100100×100=3.275%\text{Percentage Gain}=\frac{\text{SP}-\text{CP}}{\text{CP}}\times 100=\frac{103.275-100}{100}\times 100=3.275%Percentage Gain=CPSP−CP×100=100103.275−100×100=3.275%
Conclusion:
The shopkeeper makes a 3.27% gain by increasing the price by 35% and then
offering two successive discounts of 10% and 15%
If you need the formula for two successive discounts, it is:
Net Discount=a+b−ab100\text{Net Discount}=a+b-\frac{ab}{100}Net Discount=a+b−100ab
where aaa and bbb are the discount percentages.
But for profit/loss, always compare the final selling price to the original cost price.
