Commerce questions become clear once three prices are kept distinct. Cost price (CP) is what the seller pays. Marked price (MP) is the displayed price before discount. Selling price (SP) is what the customer actually pays. Profit and loss compare SP with CP; discount compares MP with SP. Their percentage bases are therefore different.
1. Build the price chain
Profit = SP−CP when SP exceeds CP; loss = CP−SP when SP is lower. Profit percentage = profit/CP×100 and loss percentage = loss/CP×100. Discount = MP−SP; discount percentage = discount/MP×100. A 20% discount is never automatically a 20% loss. A shop may set MP above CP and still make a profit after discount.
Write the chain CP → MP → SP. A markup of m% gives MP=CP(1+m/100). A discount of d% gives SP=MP(1−d/100). Multiplying these factors gives SP directly from CP. If tax is added after the discount, it applies to the discounted amount unless the question specifies another base.
Worked example 1. A product costs ₹800, is marked 25% above cost and sold after a 10% discount. MP=800×1.25=₹1,000. SP=1,000×0.90=₹900. Profit is ₹100, or 100/800=12.5% of cost. Markup minus discount, 25−10=15%, is not the profit rate because the discount uses MP as its base.
2. Recover an unknown price
If a seller makes 15% profit, SP=1.15CP and CP=SP/1.15. If a seller incurs 15% loss, SP=0.85CP and CP=SP/0.85. Never subtract 15% of the selling price to recover CP; the given percentage was based on cost. When the question gives a profit amount and a rate, CP=profit/(rate/100).
Worked example 2. An article sells for ₹1,380 at 15% profit. Its cost was 1,380/1.15=₹1,200. The difference is ₹180, which is exactly 15% of ₹1,200.
3. Successive discounts and markups
Two discounts of a% and b% leave a fraction (1−a/100)(1−b/100) of MP. Their equivalent single discount is a+b−ab/100 percent. For 20% and 10%, the equivalent is 28%, not 30%. The second discount applies to the already reduced price.
The order of multiplication does not change the final price when both changes are pure percentages, but it may change intermediate cash amounts. If the question asks how much the second discount saved, compute the first reduction first. A fixed rupee rebate does not commute with a percentage change in the same way.
Worked example 3. A jacket marked ₹2,000 receives discounts of 20% and then 10%. After the first it costs ₹1,600; the second discount is ₹160. The final price is ₹1,440, a total reduction of ₹560 or 28% of MP.
4. Equal selling prices and unequal costs
If two articles sell for the same SP, one at x% profit and the other at x% loss, the combined outcome is a loss of x²/100 percent, provided each percentage is measured on its own CP. This can be derived by taking the equal SP as a convenient value and reconstructing each CP. Do not apply the rule when the cost prices are equal; the condition matters.
Worked example 4. Each of two items sells for ₹990. One yields 10% profit, so its CP is 990/1.10=₹900. The other yields 10% loss, so its CP is 990/0.90=₹1,100. Total CP=₹2,000 and total SP=₹1,980, a 1% loss.
5. False weights and quantity errors
A seller may charge for one kilogram while delivering less. The effective cost is based on the quantity actually delivered, not the stated quantity. If a seller charges ₹100 for a “kilogram” but delivers 800 g, the received price per true kilogram is ₹125. Compare that with the seller's cost per true kilogram to compute profit. A 20% shortfall in weight is not automatically 20% profit: the actual denominator has changed.
6. Sanity checks
At 20% profit, SP must exceed CP; at 20% loss, it must be below CP. A discount lowers MP, but SP may remain above CP. Label each percentage with its base in working notes. When options are close, keep factors as fractions, such as 1.25=5/4 and 0.80=4/5, so cancellations stay exact.
Recall before practice
1. Identify the base for profit, loss and discount percentages. 2. Find the equivalent single discount of 20% followed by 10%. 3. Explain why equal 10% profit and loss at equal SP produces a net loss. 4. State how false weight changes the effective price per real kilogram.
Chapter 8 practice — 50 questions
Choose one option for each item. Keep a separate answer list; explanations follow this set.
1. 1200 lemons were bought at ₹1,130 per hundred and sold at a total profit of ₹1,040. What was the selling price per dozen?
A. ₹136 B. ₹156 C. ₹10 D. ₹146
2. A pair of shoes is marked at ₹4,600 and sold at a discount of 20%. What is its selling price?
A. ₹920 B. ₹4,580 C. ₹3,680 D. ₹5,520
3. A merchant marks his goods 100% above the cost price and allows a discount of 10%. What is his gain or loss per cent?
A. 100% gain B. 80% loss C. 80% gain D. 90% gain
4. A trader buys shirts at prices between ₹145 and ₹195 each and sells them at prices between ₹255 and ₹305 each. What is the greatest possible profit on 12 shirts?
A. ₹1,920 B. ₹160 C. ₹720 D. ₹1,320
5. Priya bought a second-hand bike for ₹4,000 and spent ₹3,000 on its servicing. At what price should it be sold to gain 20%?
A. ₹7,800 B. ₹4,800 C. ₹8,400 D. ₹9,000
6. 600 lemons were bought at ₹950 per hundred and sold at a total profit of ₹1,750. What was the selling price per dozen?
A. ₹35 B. ₹149 C. ₹114 D. ₹159
7. By selling 48 notebooks, a merchant gains an amount equal to the selling price of 24 notebooks. What is his gain per cent?
A. 100% loss B. 100% gain C. 33⅓% gain D. 50% gain
8. A shopkeeper marks his goods 100% above the cost price and allows a discount of 20%. What is his gain or loss per cent?
A. 100% gain B. 80% gain C. 60% gain D. 60% loss
9. A merchant professes to sell wheat at the cost price but uses a 750 g weight in place of 1 kg. What is his actual gain or loss per cent?
A. 33⅓% gain B. 33⅓% loss C. 25% gain D. 26% gain
10. A pair of shoes is marked at ₹1,000 and sold at a discount of 50%. What is the amount of discount?
A. ₹20 B. ₹500 C. ₹1,000 D. ₹400
11. 1800 oranges were bought at ₹1,160 per hundred and sold at a total profit of ₹5,820. What was the selling price per dozen?
A. ₹188 B. ₹39 C. ₹178 D. ₹139
12. A dealer professes to sell wheat at the cost price but uses a 640 g weight in place of 1 kg. What is his actual gain or loss per cent?
A. 56.25% loss B. 37% gain C. 36% gain D. 56.25% gain
13. Asha bought a plot of land for ₹14,000 and spent ₹2,000 on its registration and fencing. At what price should it be sold to gain 10%?
A. ₹17,400 B. ₹17,000 C. ₹15,400 D. ₹17,600
14. 1800 oranges were bought at ₹1,110 per hundred and sold at a total profit of ₹3,570. What was the selling price per dozen?
A. ₹133 B. ₹157 C. ₹24 D. ₹167
15. Vikas bought a mixer for ₹14,100 and sold it for ₹16,215. Find the gain or loss per cent.
A. 15% loss B. 15% gain C. 21.15% gain D. 20% gain
16. A fan is marked at ₹4,800 and sold at a discount of 15%. What is the amount of discount?
A. ₹720 B. ₹1,440 C. ₹4,080 D. ₹320
17. Meena bought an old car for ₹11,000, spent ₹2,000 on its repairs and sold it for ₹14,300. What is the profit per cent?
A. 30% B. 15% C. 11% D. 10%
18. A mobile phone marked at ₹2,400 is sold after successive discounts of 35% and 45%. What is its selling price?
A. ₹1,542 B. ₹1,560 C. ₹858 D. ₹480
19. Rekha bought an old car for ₹60,000, spent ₹2,000 on its repairs and sold it for ₹86,800. What is the profit per cent?
A. 45% B. 41% C. 44⅔% D. 40%
20. A sofa set with a marked price of ₹3,800 is sold at a discount of ₹760. What is the discount per cent?
A. 20% B. 25% C. 40% D. 80%
21. 300 bananas were bought at ₹860 per hundred and sold at a total profit of ₹445. What was the selling price per dozen?
A. ₹121 B. ₹103 C. ₹18 D. ₹131
22. A cooler is sold at a loss of 10%. Had it been sold for ₹1,925 more, there would have been a gain of 15%. What is the cost price?
A. ₹9,625 B. ₹19,250 C. ₹38,500 D. ₹7,700
23. 1500 eggs were bought at ₹1,290 per hundred and sold at a total profit of ₹775. What was the selling price per dozen?
A. ₹171 B. ₹6 C. ₹155 D. ₹161
24. A trader marks his goods 75% above the cost price and earns a profit of 54% after allowing a discount. What is the discount per cent?
A. 88% B. 12% C. 14% D. 21%
25. After allowing a discount of 12% on the marked price, a merchant still gains 10%. What is the ratio of the cost price to the marked price?
A. 50 : 61 B. 4 : 5 C. 5 : 4 D. 45 : 56
26. Amit bought a scooter for ₹3,650 and sold it for ₹3,942. Find the gain or loss per cent.
A. 8% loss B. 8% gain C. 13% gain D. 2.92% gain
27. A merchant marks his goods 50% above the cost price and earns a profit of 32% after allowing a discount. What is the discount per cent?
A. 12% B. 88% C. 14% D. 18%
28. Neha bought an old car for ₹22,000 and spent ₹2,000 on its repairs. At what price should it be sold to gain 4%?
A. ₹24,960 B. ₹22,880 C. ₹24,880 D. ₹24,400
29. A mobile phone is marked at ₹2,300 and sold at a discount of 5%. What is its selling price?
A. ₹115 B. ₹2,415 C. ₹2,295 D. ₹2,185
30. On selling a television, a shopkeeper earns a profit of ₹3,425, which is 25% of the cost price. What is the cost price?
A. ₹13,700 B. ₹10,275 C. ₹17,125 D. ₹34,250
31. After allowing a discount of 20% on the marked price, a shopkeeper still gains 30%. What is the ratio of the cost price to the marked price?
A. 7 : 12 B. 13 : 8 C. 8 : 13 D. 2 : 3
32. A table sold for ₹12,056 gives a loss of 12%. At what price should it be sold to gain 12%?
A. ₹13,810 B. ₹15,344 C. ₹16,988 D. ₹13,700
33. At what price should a laptop costing ₹8,900 be marked so that after allowing a discount of 20% the seller still gains 40%?
A. ₹14,952 B. ₹12,460 C. ₹14,240 D. ₹15,575
34. A table is marked at ₹19,600. A customer first gets a flat ₹200 off and then a further discount of 20% on the reduced price. How much does the customer pay?
A. ₹15,720 B. ₹15,481 C. ₹15,480 D. ₹15,520
35. A trader sells 12 glasses for ₹1,056 at a profit of 10%. How many glasses should he sell for ₹2,688 to earn a profit of 5%?
A. 30 B. 34 C. 32 D. 31
36. A laptop marked at ₹19,700 is sold after successive discounts of 16% and 50%. What is its selling price?
A. ₹8,274 B. ₹11,426 C. ₹6,698 D. ₹16,548
37. A fan is sold at a gain of 5%. Had it been sold for ₹60 more, there would have been a gain of 20%. What is the cost price?
A. ₹1,200 B. ₹240 C. ₹300 D. ₹400
38. A sofa set is marked at ₹5,750 and sold at a discount of 60%. What is the amount of discount?
A. ₹3,450 B. ₹2,300 C. ₹6,900 D. ₹4,140
39. Mohan bought a second-hand bike for ₹13,000 and spent ₹500 on its servicing. At what price should it be sold to gain 24%?
A. ₹16,620 B. ₹16,120 C. ₹16,740 D. ₹15,900
40. A laptop is sold to one customer at a discount of 10% and to another at a discount of 45%. If the two customers paid amounts differing by ₹525, what is the marked price?
A. ₹3,000 B. ₹1,500 C. ₹5,250 D. ₹1,800
41. Asha bought a scooter for ₹23,000, spent ₹1,000 on its transportation and sold it for ₹27,600. What is the profit per cent?
A. 19⅙% B. 20% C. 16% D. 15%
42. A fruit-seller buys eggs at ₹875 per hundred. At what price per dozen should he sell them to gain 20%?
A. ₹84 B. ₹138 C. ₹126 D. ₹105
43. Two watches were bought for ₹33,000 together. One was sold at a loss of 25% and the other at a gain of 5%, and there was no overall gain or loss. What was the cost price of the watch sold at a loss?
A. ₹27,500 B. ₹5,500 C. ₹5,450 D. ₹16,500
44. Two watches were bought for ₹51,750 together. One was sold at a loss of 20% and the other at a gain of 25%, and there was no overall gain or loss. What was the cost price of the watch sold at a loss?
A. ₹25,875 B. ₹28,750 C. ₹28,700 D. ₹23,000
45. Anita bought a scooter for ₹55,000, spent ₹2,000 on its transportation and sold it for ₹62,700. What is the profit per cent?
A. 15% B. 10% C. 11% D. 14%
46. After allowing a discount of 12% on the marked price, a dealer still gains 10%. What is the ratio of the cost price to the marked price?
A. 5 : 4 B. 4 : 5 C. 50 : 61 D. 45 : 56
47. A fruit-seller buys eggs at ₹1,100 per hundred. At what price per dozen should he sell them to gain 25%?
A. ₹132 B. ₹177 C. ₹99 D. ₹165
48. A merchant sells 10 pens for ₹660 at a profit of 10%. How many pens should he sell for ₹2,457 to earn a profit of 5%?
A. 41 B. 14 C. 39 D. 37
49. Successive discounts of 5%, 50% and 20% are equivalent to a single discount of:
A. 75% B. 62% C. 74% D. 77.5%
50. A table was sold at a gain of 5%. Had it been bought for 25% less and sold for ₹150 more, there would have been a gain of 60%. Find the original cost price.
A. ₹1,150 B. ₹750 C. ₹1,000 D. ₹250
Chapter 8 — Answers and explanations
After checking the key, re-solve any miss without looking at the formula.
1. D. Total CP = (1200/100) × ₹1,130 = ₹13,560. Total SP = CP + profit = ₹13,560 + ₹1,040 = ₹14,600. Number of dozens = 1200/12 = 100, so SP per dozen = ₹14,600/100 = ₹146.
APAR26-08-04 | Bought per hundred, sold per dozen | Easy
2. C. Discount = 20% of MP = 20/100 × ₹4,600 = ₹920. Selling price = MP − discount = ₹4,600 − ₹920 = ₹3,680. So SP = ₹3,680.
APAR26-08-03 | Single discount | Easy
3. C. Let CP = ₹100. MP = ₹200. SP = 200 × 90/100 = ₹180. Net = 80% gain. Formula: m − d − md/100 = 100 − 10 − 10 = 80%. (Simply taking 100 − 10 = 90% ignores the cross term.)
APAR26-08-05 | Markup then discount | Easy
4. A. Greatest profit per item = highest SP − lowest CP = ₹305 − ₹145 = ₹160. On 12 items: ₹160 × 12 = ₹1,920. (Least profit would pair the lowest SP with the highest CP: ₹720.)
APAR26-08-02 | Maximum possible profit from price ranges | Easy
5. C. Effective CP = purchase + overheads = ₹4,000 + ₹3,000 = ₹7,000. SP for 20% gain = ₹7,000 × 120/100 = ₹8,400. (Applying 20% to ₹4,000 alone and then adding ₹3,000 gives ₹7,800, which is wrong.)
APAR26-08-08 | Overheads included in cost | Easy
6. B. Total CP = (600/100) × ₹950 = ₹5,700. Total SP = CP + profit = ₹5,700 + ₹1,750 = ₹7,450. Number of dozens = 600/12 = 50, so SP per dozen = ₹7,450/50 = ₹149.
APAR26-08-01 | Bought per hundred, sold per dozen | Easy
7. B. Let SP of 1 item = ₹1. SP of 48 = ₹48; profit = SP of 24 = ₹24, so CP = 48 − 24 = ₹24. Profit% = 24/24 × 100 = 100% gain. (Dividing by 48 instead of the CP 24 is the trap.)
APAR26-08-15 | Gain equal to SP of k items | Easy
8. C. Let CP = ₹100. MP = ₹200. SP = 200 × 80/100 = ₹160. Net = 60% gain. Formula: m − d − md/100 = 100 − 20 − 20 = 60%. (Simply taking 100 − 20 = 80% ignores the cross term.)
APAR26-08-07 | Markup then discount | Easy
9. A. He charges for 1000 g at 100% of CP but gives only 750 g. Gain% = (SP factor ÷ weight factor − 1) × 100 = (100/100 × 1000/750 − 1) × 100 = ((1000 − 750)/750) × 100 = 33⅓% gain. (Taking the weight shortfall 25% as the profit is the usual trap: profit is reckoned on what he actually gives.)
APAR26-08-09 | Dishonest dealer (false weight) | Easy
10. B. Discount = 50% of MP = 50/100 × ₹1,000 = ₹500. Selling price = MP − discount = ₹1,000 − ₹500 = ₹500. So the discount is ₹500.
APAR26-08-06 | Single discount | Easy
11. C. Total CP = (1800/100) × ₹1,160 = ₹20,880. Total SP = CP + profit = ₹20,880 + ₹5,820 = ₹26,700. Number of dozens = 1800/12 = 150, so SP per dozen = ₹26,700/150 = ₹178.
APAR26-08-14 | Bought per hundred, sold per dozen | Easy
12. D. He charges for 1000 g at 100% of CP but gives only 640 g. Gain% = (SP factor ÷ weight factor − 1) × 100 = (100/100 × 1000/640 − 1) × 100 = ((1000 − 640)/640) × 100 = 56.25% gain. (Taking the weight shortfall 36% as the profit is the usual trap: profit is reckoned on what he actually gives.)
APAR26-08-12 | Dishonest dealer (false weight) | Easy
13. D. Effective CP = purchase + overheads = ₹14,000 + ₹2,000 = ₹16,000. SP for 10% gain = ₹16,000 × 110/100 = ₹17,600. (Applying 10% to ₹14,000 alone and then adding ₹2,000 gives ₹17,400, which is wrong.)
APAR26-08-11 | Overheads included in cost | Easy
14. B. Total CP = (1800/100) × ₹1,110 = ₹19,980. Total SP = CP + profit = ₹19,980 + ₹3,570 = ₹23,550. Number of dozens = 1800/12 = 150, so SP per dozen = ₹23,550/150 = ₹157.
APAR26-08-10 | Bought per hundred, sold per dozen | Easy
15. B. Profit = ₹16,215 − ₹14,100 = ₹2,115. Profit% = ₹2,115/₹14,100 × 100 = 15% — always on the cost price, never on the selling price.
APAR26-08-13 | Profit / loss per cent from CP and SP | Easy
16. A. Discount = 15% of MP = 15/100 × ₹4,800 = ₹720. Selling price = MP − discount = ₹4,800 − ₹720 = ₹4,080. So the discount is ₹720.
APAR26-08-21 | Single discount | Medium
17. D. Total CP = ₹11,000 + ₹2,000 = ₹13,000 (overheads are part of the cost). Profit = ₹14,300 − ₹13,000 = ₹1,300. Profit% = ₹1,300/₹13,000 × 100 = 10%. (Ignoring the ₹2,000 gives 30%.)
APAR26-08-35 | Overheads included in cost | Medium
18. C. SP = MP × 65/100 × 55/100 = ₹2,400 × 65/100 × 55/100 = ₹858. (Adding the discounts to 80% and taking ₹480 is the trap: each discount applies to the already-reduced price.)
APAR26-08-33 | Successive discounts | Medium
19. D. Total CP = ₹60,000 + ₹2,000 = ₹62,000 (overheads are part of the cost). Profit = ₹86,800 − ₹62,000 = ₹24,800. Profit% = ₹24,800/₹62,000 × 100 = 40%. (Ignoring the ₹2,000 gives 44⅔%.)
APAR26-08-39 | Overheads included in cost | Medium
20. A. Discount% is always reckoned on the marked price: ₹760/₹3,800 × 100 = 20%. (Dividing by the selling price ₹3,040 instead of the MP is the common error.)
APAR26-08-31 | Single discount | Medium
21. A. Total CP = (300/100) × ₹860 = ₹2,580. Total SP = CP + profit = ₹2,580 + ₹445 = ₹3,025. Number of dozens = 300/12 = 25, so SP per dozen = ₹3,025/25 = ₹121.
APAR26-08-19 | Bought per hundred, sold per dozen | Medium
22. D. Let CP = x. SP₁ = x × 90/100 and SP₂ = x × 115/100. SP₂ − SP₁ = x × (115 − 90)/100 = x × 25/100 = ₹1,925. So x = ₹1,925 × 100/25 = ₹7,700.
APAR26-08-18 | Two selling scenarios | Medium
23. D. Total CP = (1500/100) × ₹1,290 = ₹19,350. Total SP = CP + profit = ₹19,350 + ₹775 = ₹20,125. Number of dozens = 1500/12 = 125, so SP per dozen = ₹20,125/125 = ₹161.
APAR26-08-36 | Bought per hundred, sold per dozen | Medium
24. B. Let CP = 100 ⇒ MP = 175, SP = 154. Discount = MP − SP = 21 on MP 175: 21/175 × 100 = 12%. (Taking 75 − 54 = 21% directly is wrong because discount is a % of MP.)
APAR26-08-37 | Find the discount | Medium
25. B. SP = MP × (100 − 12)/100 = CP × (100 + 10)/100. Hence CP/MP = (100 − 12)/(100 + 10) = 88/110, i.e. CP : MP = 4 : 5. (Writing it the other way round, 5 : 4, is the common slip.)
APAR26-08-34 | CP : MP from discount and profit | Medium
26. B. Profit = ₹3,942 − ₹3,650 = ₹292. Profit% = ₹292/₹3,650 × 100 = 8% — always on the cost price, never on the selling price.
APAR26-08-24 | Profit / loss per cent from CP and SP | Medium
27. A. Let CP = 100 ⇒ MP = 150, SP = 132. Discount = MP − SP = 18 on MP 150: 18/150 × 100 = 12%. (Taking 50 − 32 = 18% directly is wrong because discount is a % of MP.)
APAR26-08-29 | Find the discount | Medium
28. A. Effective CP = purchase + overheads = ₹22,000 + ₹2,000 = ₹24,000. SP for 4% gain = ₹24,000 × 104/100 = ₹24,960. (Applying 4% to ₹22,000 alone and then adding ₹2,000 gives ₹24,880, which is wrong.)
APAR26-08-22 | Overheads included in cost | Medium
29. D. Discount = 5% of MP = 5/100 × ₹2,300 = ₹115. Selling price = MP − discount = ₹2,300 − ₹115 = ₹2,185. So SP = ₹2,185.
APAR26-08-32 | Single discount | Medium
30. A. Profit = 25% of CP ⇒ CP = profit × 100/25 = ₹3,425 × 100/25 = ₹13,700. (Adding the profit to this, ₹17,125, gives the selling price, not the cost price.)
APAR26-08-23 | CP from profit amount and profit % | Medium
31. C. SP = MP × (100 − 20)/100 = CP × (100 + 30)/100. Hence CP/MP = (100 − 20)/(100 + 30) = 80/130, i.e. CP : MP = 8 : 13. (Writing it the other way round, 13 : 8, is the common slip.)
APAR26-08-25 | CP : MP from discount and profit | Medium
32. B. CP = SP/(1 − 12/100) = ₹12,056 × 100/88 = ₹13,700. New SP = ₹13,700 × 112/100 = ₹15,344. (Shortcut: SP₂ = SP₁ × 112/88. Applying 12% to ₹12,056 directly gives ₹13,502.72, which is wrong.)
APAR26-08-30 | SP for target profit given loss SP | Medium
33. D. Required SP = ₹8,900 × 140/100 = ₹12,460. MP × 80/100 = SP ⇒ MP = ₹12,460 × 100/80 = ₹15,575. (Marking 40% + 20% = 60% above cost, ₹14,240, falls short.)
APAR26-08-28 | Marked price for target profit after discount | Medium
34. D. Apply in the stated order. After the flat cut: ₹19,600 − ₹200 = ₹19,400. Then × 80/100 = ₹15,520. (Applying the % discounts first and the ₹200 last gives ₹15,480, a different amount.)
APAR26-08-20 | Flat cash discount then percentage discounts | Medium
35. C. CP of 12 glasses = ₹1,056 × 100/110 = ₹960, so CP per item = ₹80. For 5% profit, SP per item = ₹80 × 105/100 = ₹84. Number = ₹2,688 ÷ ₹84 = 32. (Using the old SP per item, ₹88, gives 30.55.)
APAR26-08-17 | Number of items for a target profit | Medium
36. A. SP = MP × 84/100 × 50/100 = ₹19,700 × 84/100 × 50/100 = ₹8,274. (Adding the discounts to 66% and taking ₹6,698 is the trap: each discount applies to the already-reduced price.)
APAR26-08-26 | Successive discounts | Medium
37. D. Let CP = x. SP₁ = x × 105/100 and SP₂ = x × 120/100. SP₂ − SP₁ = x × (120 − 105)/100 = x × 15/100 = ₹60. So x = ₹60 × 100/15 = ₹400.
APAR26-08-27 | Two selling scenarios | Medium
38. A. Discount = 60% of MP = 60/100 × ₹5,750 = ₹3,450. Selling price = MP − discount = ₹5,750 − ₹3,450 = ₹2,300. So the discount is ₹3,450.
APAR26-08-40 | Single discount | Medium
39. C. Effective CP = purchase + overheads = ₹13,000 + ₹500 = ₹13,500. SP for 24% gain = ₹13,500 × 124/100 = ₹16,740. (Applying 24% to ₹13,000 alone and then adding ₹500 gives ₹16,620, which is wrong.)
APAR26-08-38 | Overheads included in cost | Medium
40. B. Prices paid: MP × 90/100 and MP × 55/100. Difference = MP × (45 − 10)/100 = MP × 35/100 = ₹525 ⇒ MP = ₹525 × 100/35 = ₹1,500.
APAR26-08-16 | Two buyers, two discounts | Medium
41. D. Total CP = ₹23,000 + ₹1,000 = ₹24,000 (overheads are part of the cost). Profit = ₹27,600 − ₹24,000 = ₹3,600. Profit% = ₹3,600/₹24,000 × 100 = 15%. (Ignoring the ₹1,000 gives 20%.)
APAR26-08-48 | Overheads included in cost | Difficult
42. C. CP per dozen = ₹875 × 12/100 = ₹105. For 20% gain, SP per dozen = ₹105 × 120/100 = ₹126.
APAR26-08-47 | Per-dozen price for a target profit | Difficult
43. B. Let the first cost x, the second ₹33,000 − x. Loss on first = gain on second: x × 25/100 = (₹33,000 − x) × 5/100 ⇒ x : (₹33,000 − x) = 5 : 25. So x = ₹33,000 × 5/30 = ₹5,500 (and the other cost ₹27,500).
APAR26-08-41 | No overall gain or loss | Difficult
44. B. Let the first cost x, the second ₹51,750 − x. Loss on first = gain on second: x × 20/100 = (₹51,750 − x) × 25/100 ⇒ x : (₹51,750 − x) = 25 : 20. So x = ₹51,750 × 25/45 = ₹28,750 (and the other cost ₹23,000).
APAR26-08-45 | No overall gain or loss | Difficult
45. B. Total CP = ₹55,000 + ₹2,000 = ₹57,000 (overheads are part of the cost). Profit = ₹62,700 − ₹57,000 = ₹5,700. Profit% = ₹5,700/₹57,000 × 100 = 10%. (Ignoring the ₹2,000 gives 14%.)
APAR26-08-49 | Overheads included in cost | Difficult
46. B. SP = MP × (100 − 12)/100 = CP × (100 + 10)/100. Hence CP/MP = (100 − 12)/(100 + 10) = 88/110, i.e. CP : MP = 4 : 5. (Writing it the other way round, 5 : 4, is the common slip.)
APAR26-08-46 | CP : MP from discount and profit | Difficult
47. D. CP per dozen = ₹1,100 × 12/100 = ₹132. For 25% gain, SP per dozen = ₹132 × 125/100 = ₹165.
APAR26-08-42 | Per-dozen price for a target profit | Difficult
48. C. CP of 10 pens = ₹660 × 100/110 = ₹600, so CP per item = ₹60. For 5% profit, SP per item = ₹60 × 105/100 = ₹63. Number = ₹2,457 ÷ ₹63 = 39. (Using the old SP per item, ₹66, gives 37.23.)
APAR26-08-43 | Number of items for a target profit | Difficult
49. B. Take MP = 100. Price paid = 100 × 95/100 × 50/100 × 80/100 = 38. Single equivalent discount = 100 − 38 = 62%. (Apply a + b − ab/100 twice. The plain sum 75% overstates the discount.)
APAR26-08-44 | Equivalent single discount | Difficult
50. C. Let CP = ₹100. SP₁ = ₹105. New CP = ₹75, new SP = 75 × 160/100 = ₹120. New SP − SP₁ = 15 units = ₹150, so 100 units = ₹150 × 100/15 = ₹1,000. (Check: new CP ₹750, new SP ₹1,200.)
APAR26-08-50 | Changed cost and selling price | Difficult