A seller sold an article with 20% loss. If he sold the article with Rs. 200 more he would have a profit of 5%. Cost price of the article was:

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PREVIOUSLY ASKED IN:
PSC Miscellaneous Prelims 2018

Answer

Rs. 800

Explanation

Let the Cost Price (CP) of the article be 100%. Initially, the seller sold it at a 20% loss, making the Selling Price (SP) 80%. If sold for Rs. 200 more, there would be a 5% profit, making the new SP 105%. The difference in percentage between the two selling prices is 105% - 80% = 25%. This 25% difference is equal to Rs. 200. Therefore, 100% (the CP) is (200 / 25) × 100 = Rs. 800.

Key Points

  • > Always assume the Cost Price (CP) to be 100%.
  • > Loss is subtracted from CP, and profit is added to CP.
  • > First SP = 80% (20% loss), Second SP = 105% (5% profit).
  • > The difference in percentage is 25%.
  • > 25% represents the Rs. 200 price increase.
  • > 1% = 200/25 = Rs. 8.
  • > Therefore, CP (100%) = 8 × 100 = Rs. 800.

Additional Information

Key Profit & Loss Formulas

ConceptFormula
Profit Percentage(Total Profit / Cost Price) × 100
Loss Percentage(Total Loss / Cost Price) × 100
Finding CP (when Profit)[100 / (100 + Profit%)] × SP
Finding CP (when Loss)[100 / (100 - Loss%)] × SP

Memory Tips

  • Shortcut (Opposite Conditions): When transitioning from a loss to a profit, simply add the two percentages (20% + 5% = 25%). Set this sum equal to the absolute increase in price (25% = Rs. 200) to find 100%.
Mathematics Profit and Loss Medium

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