Essential Profit and Loss Formulas and Solved Examples

Profit and Loss Fundamentals

Formula: Profit or Gain = S.P. – C.P.

• Loss: If the selling price is less than the cost price, the difference between them is the loss incurred.

Formula: Loss = Cost Price (C.P.) – Selling Price (S.P.)

• Profit or Loss is always calculated on the cost price.
• Marked Price: The price marked as the selling price on an article, also known as the listed price.
• Discount or Rebate: The reduction in price offered on the marked or listed price.

Basic Profit and Loss Formulas

Below is a list of essential formulas used in solving profit and loss problems:

• Gain % = (Gain / CP) × 100
• Loss % = (Loss / CP) × 100
• SP = [(100 + Gain%) / 100] × CP
• SP = [(100 – Loss %) / 100] × CP

The above two formulas can be simplified as:

• If an article is sold at a gain of 10%, then SP = 110% of CP.
• If an article is sold at a loss of 10%, then SP = 90% of CP.
• CP = [100 / (100 + Gain%)] × SP
• CP = [100 / (100 – Loss%)] × SP

Profit and Loss: Solved Examples

Example 1

Question: 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 %.

Example 2

Question: 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.

Example 3

Question: In a transaction, the profit percentage is 80% of the cost. If the cost increases by 20% but the selling price remains the same, what is the decrease in profit percentage?

Solution: Assume CP = Rs. 100. Then Profit = Rs. 80 and SP = Rs. 180. If cost increases by 20%, New CP = Rs. 120, SP = Rs. 180. New Profit % = (60/120) × 100 = 50%. Therefore, profit decreases by 30%.

Example 4

Question: A man bought toys at 10 for Rs. 40 and sold them at 8 for Rs. 35. Find his gain or loss percent.

Solution: CP of 1 toy = Rs. 4. SP of 1 toy = 35/8. Gain = 35/8 – 4 = 3/8. Gain percent = (3/8) / 4 × 100 = 9.375%.

Example 5

Question: The cost price of 10 pens is the same as the selling price of n pens. If there is a loss of 40%, what is the value of n?

Solution: Let the price of each pen be Re. 1. CP of n pens = Rs. n, SP of n pens = Rs. 10. Loss = n – 10. Loss of 40% implies [(n – 10) / n] × 100 = 40, resulting in n = 17 (approx).

Example 6

Question: A dishonest merchant uses weights 15% less than true weights and makes a profit of 20%. Find his total gain percentage.

Solution: Consider 1 kg (1000g). Actual weight used = 850g. CP of 850g = Rs. 850. SP of 1 kg = 120% of 1000 = Rs. 1200. Gain = 1200 – 850 = 350. Gain % = (350/850) × 100 = 41.17%.