Given:
Profit percentage = 20% (On selling price)
Concept :
Profit = Selling Price (SP)– Cost Price (CP)
Profit% = (Profit/CP) × 100
Calculation:
Let selling price = Rs.100
Profit percentage = 20% (On selling price)
⇒ Profit percentage = 20% × 100 ⇒ Rs. 20
Selling Price = Cost Price + Profit
⇒ Cost price = Rs. (100 - 20) = Rs. 80
Profit percentage on cost price =Profit/Cost Price× 100
⇒Profit% = 20/80× 100 = 25%
∴ The actual percentage profit is25%.
![[Solved] There is 20% profit after selling the goods. He calculated t (1)](https://i0.wp.com/storage.googleapis.com/tb-img/production/21/12/5f804a6a2754486dfd697ff8_16391596076321.png "[Solved] There is 20% profit after selling the goods. He calculated t (1)")
Let the CP be x
Let theSP be y
So, whenthe profit is calculated on the SP, we get:
[(y – x)/y]× 100 = 20
⇒y – x = 0.2y
⇒ x = 0.8y
⇒ y/x = 1.25 ----(i)
Hence, the actual Profit will be calculated on the CP as:
Actual Profit = [(y – x)/x]× 100
⇒ Actual Profit = [(y/x)– 1]× 100
Hence, from equation (i),
∴Actual Profit = [1.25– 1]× 100 = 25%
![[Solved] There is 20% profit after selling the goods. He calculated t (2)](https://i0.wp.com/cdn.testbook.com/resources/lms_creative_elements/mistake-point-image.png "[Solved] There is 20% profit after selling the goods. He calculated t (2)")
Mistake Points
In this question we have found the profit on selling price. Not cost price. If youare taking CP = 100, then in this case you are not sure about the selling priceand profit %.
![[Solved] There is 20% profit after selling the goods. He calculated t (2024)](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAQAAAC1HAwCAAAAC0lEQVR42mP8/h8AAvMB+NzmkbcAAAAASUVORK5CYII=)