Successive Selling: Formula, Rules and Solved Problems

Successive Selling refers to an item being sold two or more times in sequence, with each sale based on the previous selling price. The final price is found by multiplying the successive profit or loss factors. This page covers the selling price chain, successive selling formula, mixed profit-loss cases and numerical examples.

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What Is Successive Selling?

Successive selling is the sale of an item through two or more transactions, where the selling price in one transaction becomes the cost price for the next transaction.

For a profit of p%, multiply the current price by 1 + p/100. For a loss of l%, multiply it by 1 − l/100. If the initial cost price is C and the successive factors are m₁, m₂, ..., mₙ, then the final selling price is C × m₁ × m₂ × ... × mₙ. The overall profit or loss percentage is found by comparing the final price with C.

Successive Selling Formula & Tricks

Important Formulas

General successive selling formula
Final SP = Initial CP × ∏(1 ± rᵢ/100)

Use + for a profit rate and − for a loss rate at each sale. Each factor applies to the price obtained in the previous sale.

Two successive profits
Net profit% = p + q + (pq/100)

If an item is sold at profits of p% and q% successively, the total profit percentage is p + q + pq/100.

Two successive losses
Net loss% = l + m − (lm/100)

If an item is sold at losses of l% and m% successively, the total loss percentage is l + m − lm/100.

Profit followed by loss
Net change% = p − l − (pl/100)

A profit of p% followed by a loss of l% gives a net profit if the result is positive and a net loss if it is negative.

Overall percentage change
Overall change% = [(Final SP − Initial CP)/Initial CP] × 100

A positive value indicates profit and a negative value indicates loss.

Quick Tricks

Use multipliers instead of repeated percentage calculations

Convert every profit or loss into a multiplier and multiply the factors in order. This keeps the changing base price correct.

Example: For profits of 20% and 10%, use 1.20 × 1.10 = 1.32. The overall profit is 32%.
Check the order in mixed cases

For only two percentage changes, the product is unchanged if the order is reversed. However, when a question gives intermediate prices or different transaction conditions, apply the stated order to each price.

Example: A 20% profit followed by a 10% loss gives 1.20 × 0.90 = 1.08, or 8% profit. A 10% loss followed by a 20% profit also gives 0.90 × 1.20 = 1.08.

Successive Selling Concepts

Selling Price Chain

In a selling price chain, the final selling price from one transaction becomes the cost price for the next transaction.

If the original cost price is C, and the first seller earns p₁% profit, the first selling price is C(1 + p₁/100). If the next seller earns p₂% profit, the next selling price is C(1 + p₁/100)(1 + p₂/100). Continue multiplying the corresponding factors for every sale.

Example: If the original CP is ₹1,000 and two sellers earn 10% and 20%, the prices are ₹1,100 and ₹1,320. The final selling price is ₹1,320.

Successive Profits

Successive profits are multiplied, not directly added, because the second profit is calculated on the increased price.

For profits of p% and q%, the final price is CP × (1 + p/100)(1 + q/100). Expanding the factors gives a net profit of p + q + pq/100 percent.

Example: For successive profits of 25% and 20%, net profit = 25 + 20 + (25 × 20)/100 = 50%. A CP of ₹800 becomes ₹1,200.

Successive Losses

Successive losses are applied to successively reduced prices, so the net loss is less than the direct sum of the two loss percentages.

For losses of l% and m%, the final price is CP × (1 − l/100)(1 − m/100). Therefore, net loss = l + m − lm/100 percent.

Example: For losses of 20% and 10%, net loss = 20 + 10 − 2 = 28%. A CP of ₹1,000 becomes ₹720.

Mixed Profit and Loss

For a profit followed by a loss, multiply the profit factor by the loss factor and compare the result with 1.

A p% profit followed by an l% loss gives the factor (1 + p/100)(1 − l/100). The net change is p − l − pl/100 percent. If the factor is greater than 1, there is a profit; if it is less than 1, there is a loss.

Example: A 30% profit followed by a 20% loss gives 1.30 × 0.80 = 1.04. Hence, the net profit is 4%.

Finding the Initial Cost Price

To find the initial cost price, divide the final selling price by the product of all successive multipliers.

If the final price is F and the successive factors are m₁, m₂, ..., mₙ, then Initial CP = F/(m₁m₂...mₙ). For a profit use 1 + percentage/100, and for a loss use 1 − percentage/100.

Example: An item is sold at 20% profit and then 10% profit for ₹1,320. Initial CP = 1,320/(1.20 × 1.10) = ₹1,000.

Successive Selling Video Lessons

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Same Selling Price: Hidden Net Loss

Learn how selling two items at the same selling price can result in a net loss, and understand the calculation method behind this Profit & Loss trap.

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Practice Successive Selling Questions

Practise published questions related to this topic.

1Find the effective price percentage of the marked price after three consecutive discounts of 10%, 27% and 8% (rounded off to two decimal places).→ 2A dealer marks his goods at 57% above the cost price and allows a discount of 22% on the marked price. What is his gain percentage (correct to two decimal places)?→ 3A person sells an article at the loss of 10 percent. Cost price and selling price both are increased by 20 percent. What will be the new loss percentage?→ 4A dealer marks his goods at 25% above the cost price and allows a discount of 28% on the marked price. What is his gain or loss percentage?→ 5An item is sold for ₹7,200 after two successive discounts of 36% and 10%. What is the marked price (in ₹) of the item?→ 6The original price of a refrigerator was $1,500. During a clearance sale, it was initially discounted by 30%, followed by an additional 10% discount on the reduced price. What is the total percentage discount applied to the refrigerator?→ 7Two successive discounts of 50 percent and 30 percent are given on an article. What is the net discount?→ 8Selling price and cost price of an article is Rs. 920 and Rs. 800 respectively. What is the profit percentage?→ 9The marked price of a cooker is the same at four shops I, II, III and IV. Shop I allows two successive discounts of 89% and 68%, shop II allows successive discounts of 50% and 51%, shop III allows successive discounts of 25% and 11% and shop IV allows successive discounts of 94%, 49%, and 21% on the marked price of the cooker. Which shop is selling the cooker at the lowest price?→ 10A mobile phone is marked at ₹8,000. If two successive discounts of 15% and 10% are given, what is the selling price?→

Successive Selling Quick Quiz

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Quick Revision Notes

Successive Selling Revision Points

Use these rules to solve successive sale questions accurately.

  • The next transaction's cost price is the previous transaction's selling price.
  • Profit of p% gives multiplier 1 + p/100.
  • Loss of l% gives multiplier 1 − l/100.
  • Final SP = Initial CP × product of all successive multipliers.
  • Two successive profits p% and q% give net profit p + q + pq/100 percent.
  • Two successive losses l% and m% give net loss l + m − lm/100 percent.
  • For mixed changes, multiply the profit and loss factors before finding the net percentage.
  • To find the initial CP, divide the final SP by the product of the successive multipliers.

Successive Selling FAQs

What is the formula for successive selling?

Final SP = Initial CP × ∏(1 ± rᵢ/100). Use a plus sign for each profit and a minus sign for each loss.

What is the net profit for successive profits of 10% and 20%?

Net profit = 10 + 20 + (10 × 20)/100 = 32%.

What is the net loss for successive losses of 15% and 20%?

Net loss = 15 + 20 − (15 × 20)/100 = 32%.

An item is sold at 25% profit and then 20% loss. What is the net result?

The multiplier is 1.25 × 0.80 = 1. Therefore, there is no profit and no loss.

An item is sold twice at 20% profit each time. What is the overall profit?

Overall multiplier = 1.20 × 1.20 = 1.44, so the overall profit is 44%, not 40%.

An item is finally sold for ₹1,560 after profits of 20% and 30%. What was its initial cost price?

Initial CP = 1,560/(1.20 × 1.30) = ₹1,000.

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