How to Solve Successive Profit and Loss Transactions
Solve successive profit and loss aptitude problems using chained multipliers and the a+b+ab/100 shortcut, with worked examples and practice.
Expected Interview Answer
When an item is bought and sold multiple times in a chain, each successive profit or loss percentage multiplies onto the running price as a factor of (1 + gain/100) or (1 - loss/100), so the final price is the original cost times the product of all these factors, never a simple sum of the percentages.
Treat every successive transaction as a multiplier on the current price, not the original price: a 20% gain becomes ×1.20 and a 10% loss becomes ×0.90, applied one after another in the order given. Chain the multipliers together — Final Price = Cost × f1 × f2 × f3 × ... — and only at the end compare Final Price to Cost to get the net percentage change. A frequent trap is assuming gains and losses of equal magnitude cancel out; they do not, because the loss is applied to a larger or smaller base than the gain was. For two successive changes of a% and b%, the net percentage change is a + b + ab/100, which correctly captures this compounding effect.
- Multiplicative chaining avoids the equal-percent-cancels-out trap
- The a + b + ab/100 shortcut handles two-step chains instantly
- Generalizes cleanly to any number of successive buy-sell transactions
AI Mentor Explanation
A team's run rate rises 20% in the powerplay, then drops 10% in the middle overs — you cannot just say net change is +10%, because the 10% drop applies to the already-boosted run rate, not the original one. Multiply the factors instead: 1.20 × 0.90 = 1.08, a net 8% rise, not the naive 10%. Successive profit and loss problems work identically: each percentage change is a multiplier on the current value, chained in sequence, never added directly to the others.
Worked example (buy, sell, rebuy, resell)
After 20% gain
- 1000 × 1.20
- = 1200
After 10% loss
- 1200 × 0.90
- = 1080
Net change
- 20 - 10 - 2 = 8%
- Final = 1080
Step-by-Step Explanation
Step 1
Convert each percentage to a factor
Gain of x% becomes ×(1 + x/100); loss of x% becomes ×(1 - x/100).
Step 2
Chain the factors in order
Final Price = Cost × factor1 × factor2 × ... × factorN, applied sequentially.
Step 3
Compare final to original
Net % change = (Final Price - Cost) / Cost × 100.
Step 4
Use the two-step shortcut when applicable
For exactly two changes a% and b%, net % = a + b + ab/100.
What Interviewer Expects
- Recognition that percentages multiply as running factors, not add
- Correct sign handling for loss factors (1 - x/100)
- Application of the a + b + ab/100 shortcut for two-step chains
- Awareness that equal-magnitude gain and loss never fully cancel
Common Mistakes
- Adding the profit and loss percentages directly to get net change
- Applying every percentage to the original cost instead of the running price
- Assuming a gain and equal loss cancel to zero net change
- Sign errors when converting a loss percentage into a multiplying factor
Best Answer (HR Friendly)
“Every successive transaction is just a multiplying factor on whatever the current price is — a gain of x percent is times 1 plus x over 100, and a loss is times 1 minus x over 100. You chain these factors in the order the transactions happened and only compare the very last price to the original cost. For two steps there is a quick shortcut, a plus b plus a times b over 100, which shows why equal gains and losses never truly cancel out.”
Follow-up Questions
- How would you extend the two-step shortcut to three successive transactions?
- Why do a gain and an equal-magnitude loss never fully cancel out?
- How do you handle a successive discount problem using the same multiplier method?
- How would you find the single equivalent percentage change for a chain of five transactions?
MCQ Practice
1. An item is sold at a 25% profit, then resold at a 20% loss on the new price. What is the net percentage change from the original cost?
Net factor = 1.25 × 0.80 = 1.00, so the net change is exactly 0% — the original cost is recovered exactly.
2. Using the shortcut a + b + ab/100 for successive changes of +30% and -30%, the net change is?
30 + (-30) + (30)(-30)/100 = 0 - 9 = -9%, a net loss despite equal-magnitude percentages.
3. Cost price is 2000. It is sold at a 10% profit, then the buyer resells it at a 10% profit on the new price. Final selling price is?
2000 × 1.10 × 1.10 = 2000 × 1.21 = 2420.
Flash Cards
How do successive percentage changes combine? — Multiplicatively, as chained factors on the running price, never by addition.
Factor for a loss of x%? — (1 - x/100), multiplied onto the current price.
Two-step net change shortcut? — Net % = a + b + ab/100 for successive changes a% and b%.
Do an equal gain and loss cancel out? — No — the loss applies to a different (usually larger) base than the gain did.