0i. Cost Price: The price, at which an article is purchased, is called its cost price, abbreviated as C.P.
ii. Selling Price: The price, at which an article is sold, is called itsselling prices, abbreviated as S.P.
iii. Profit or Gain: If S.P. is greater than C.P., the seller is said to have a profit or gain.
iv. Loss: If S.P. is less than C.P., the seller is said to have incurred a loss.
Important Formulae:
- Gain % = (Gain / CP) * 100
- Loss % = (Loss / CP) * 100
- SP = [(100 + Gain%) / 100] * CP
- SP = [(100 – Loss %) / 100] * CP
- CP = [100 / (100 + Gain%)] * SP
- CP = [100 / (100 – Loss%)] * SP
Solved Examples:
Question 1: An article is purchased for Rs. 450 and sold for Rs. 500. Find the gain percent.
Solution:
Gain = SP – CP = 500 – 450 = 50.
Gain% = (50/450)*100 = 100/9 %
Question 2: A man sold a fan for Rs. 465. Find the cost price if he incurred a loss of 7%.
Solution:
CP = [100 / (100 – Loss %)] * SP
Therefore, the cost price of the fan = (100/93)*465 = Rs. 500
Question 3: In a transaction, the profit percentage is 80% of the cost. If the cost further increases by 20% but the selling price remains the same, how much is the decrease in profit percentage?
Solution:
Let us assume CP = Rs. 100.
Then Profit = Rs. 80 and selling price = Rs. 180.
The cost increases by 20% → New CP = Rs. 120, SP = Rs. 180.
Profit % = 60/120 * 100 = 50%.
Therefore, Profit decreases by 30%.
Question 4: A man bought some toys at the rate of 10 for Rs. 40 and sold them at 8 for Rs. 35. Find his gain or loss percent.
Solution:
Cost price of 10 toys = Rs. 40 → CP of 1 toy = Rs. 4.
Selling price of 8 toys = Rs. 35 → SP of 1 toy = Rs. 35/8
Therefore, Gain = 35/8 – 4 = 3/8.
Gain percent = (3/8)/4 * 100 = 9.375%
