6. Profit, loss, discount and marked price
Free study material · concepts, shortcuts & solved questions
Profit or loss is calculated on cost price unless the question says otherwise. Profit% = profit/CP ×100; loss% = loss/CP ×100. Discount is on marked price: discount% = discount/MP ×100 and SP=MP(1−d/100). For successive discounts a and b, equivalent discount = a+b−ab/100.
Method before formula Margin on selling price is a different denominator. If an item is sold at 20% profit, SP=120% of CP, so CP is 100/120 of SP. Work backward with multipliers. |
Formula and decision table
Formula | Use |
Profit | SP=CP(1+p/100) |
Loss | SP=CP(1−l/100) |
Discount | SP=MP(1−d/100) |
Two discounts | 10% and 20% => 28% equivalent |
Worked understanding
A reliable solution has five visible moves: identify the data, choose the base or unit, write the rule, substitute carefully, and check the size of the answer. The examples in this chapter are deliberately small so that the method remains visible.
Calculation discipline Before pressing ahead, state the denominator or unit in words. For example: profit on CP, discount on MP, average over number of items, speed in metres per second, and probability over the fixed sample space. |
Solved examples from this chapter
Question focus | Correct move | Answer |
CP=800, profit 15%. SP: | 800×1.15=920. | C. 920 |
MP=1000, discounts 10% and 20%. SP: | 1000×0.9×0.8=720. | B. 720 |
Profit percentage is normally calculated on: | Unless stated otherwise, the base is cost price. | B. CP |
What an examiner is testing
The options around Profit, loss, discount and marked price usually represent a wrong base, a missed conversion, a sign error or a shortcut used outside its condition. Say the base and unit before calculating, estimate the result, and use substitution or a reverse operation as the final check.
Step-by-step answer construction
Example 1: CP=800, profit 15%. SP: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 920, because 800×1.15=920.
Example 2: MP=1000, discounts 10% and 20%. SP: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 720, because 1000×0.9×0.8=720.
Example 3: Profit percentage is normally calculated on: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is CP, because Unless stated otherwise, the base is cost price.
Chapter practice
1. CP=800, profit 15%. SP:
(A) 880 (B) 900 (C) 920 (D) 940
Answer: C. 920 | Explanation: 800×1.15=920.
2. MP=1000, discounts 10% and 20%. SP:
(A) 700 (B) 720 (C) 800 (D) 820
Answer: B. 720 | Explanation: 1000×0.9×0.8=720.
3. Profit percentage is normally calculated on:
(A) SP (B) CP (C) MP (D) Tax
Answer: B. CP | Explanation: Unless stated otherwise, the base is cost price.
SSC CGL speed and trap clinic
For Profit, loss, discount and marked price, speed comes after classification. Before calculating, say aloud what the number means, what the denominator is, and what unit the answer must carry. Then use the nearest-option check to catch a sign, base or conversion error.
Checkpoint | What to verify | Typical SSC mistake |
Base | Which quantity is the base in Profit, loss, discount and marked price? | Using selling price instead of cost price, or part instead of total |
Unit | Are time, distance, area and rate in compatible units? | Mixing hours with minutes or km/h with m/s |
Direction | Should the answer increase, decrease or stay bounded? | Accepting an impossible negative length or probability above 1 |
Estimate | What range should the answer lie in before exact work? | Trusting a long calculation that is far from the options |
Reverse check | Can the answer be substituted back into the condition? | Stopping at an algebraic value without verification |
Mini decision drill
1. Write the first operation you would perform in a Profit, loss, discount and marked price question and why.
2. State the most dangerous denominator or unit in this chapter.
3. Give one condition under which a shortcut would be invalid.
4. Create a small numerical example and verify it by a second method.
Revision evidence Do not tick this chapter because you recognised the formula. Tick it only after you solve one direct question, one altered-condition question and one mixed-paper question correctly. |