Class 8 · English Version · Mathematics
2026 Class 8 Mathematics · English Version · Chapter 2 · Chapter companion part
Find full cost, profit or loss, and explain percentages, inverse prices and successive sellers.
Class 8 English Version: part A of the chapter 2 companion. Eight teaching sections, 30 written tasks and a notebook challenge. Selected companion coverage, not complete textbook coverage; use all four parts and ask a teacher to review explanations and open solutions.
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Cost price C includes the purchase price and any stated transport, packing, rent allocation or other related expense. Selling price S is what the seller receives for the same quantity. For an invented parcel bought for Tk 480 with Tk 20 transport, C = 500. A selling price of Tk 575 gives Tk 75 profit. Do not omit an expense explicitly included in the task, or add an unstated expense.
If S > C, profit G = S − C. If S < C, loss L = C − S. Equal prices give neither profit nor loss. State which quantity your positive difference represents. A Tk 50 loss on a Tk 500 cost leaves a Tk 450 selling price. A negative signed change S − C can describe a loss, but calling a negative number a positive profit is misleading.
Profit percentage is 100G/C and loss percentage is 100L/C, using cost as the base. With C = 500 and G = 75, 75/500 = 0.15 = 15%. This means Tk 15 gained per Tk 100 of cost. Dividing by selling price instead measures a different relationship. Our task uses the cost-based convention taught in this chapter.
Let R be the profit percentage number and q = R/100. At profit, S = C(1 + q), so C = S/(1 + q). At loss, S = C(1 − q), so C = S/(1 − q). For a 15% profit and S = 690, C = 690/1.15 = 600. Subtracting 15% of 690 would use the wrong base. A positive selling price cannot follow a loss of 100% or more under this ordinary model.
The same item sold at 10% loss would bring 0.90C; sold at 15% profit it would bring 1.15C. The difference is 0.25C. If that difference is Tk 200, then C = 200/0.25 = 800. The 25 percentage points describe the difference between the two cost-based rates; they are not 25% of either selling price.
Six items for Tk 30 cost Tk 5 each; five items sold for Tk 30 bring Tk 6 each. One item therefore gains Tk 1 on cost Tk 5, or 20%. A quad or hali means four items. Convert both sides to a common item count or unit price before subtracting. A lower number of items per taka means a higher price per item.
Buy equal numbers at eight pieces for Tk 24 and twelve pieces for Tk 24. Unit costs are Tk 3 and Tk 2. For equal pieces the mean unit cost is (3 + 2)/2 = 2.50; selling ten for Tk 25 breaks even. If equal amounts of money are spent, the quantities differ and the simple mean of the two unit costs is not appropriate. Show actual total cost divided by actual total pieces.
A wholesaler buys for Tk 1000 and sells at 20% profit for Tk 1200. A retailer treats Tk 1200 as cost and sells at 10% profit for Tk 1320. The combined multiplier is 1.20 × 1.10 = 1.32, giving 32% relative to the first cost. The rates do not simply add to 30%. To work backwards, divide the final price by both multipliers.
For a purchase 750 plus stated expenses 50, cost is 800. At a loss of 7.5%, loss = 800 × 0.075 = 60 and sale = 740. Check 740 + 60 = 800.
A money amount may be Tk 8; a rate is 8%. Source wording sometimes places Tk before a percentage. Keep money and rates separate.
All prices and quantities in these tasks are invented to practise the source methods. They are not current market observations.
Read the cost first, then find the signed change and divide its magnitude by cost.
| Cost (Tk) | Sale (Tk) | Result (Tk) | Percentage on cost |
|---|---|---|---|
| 500 | 575 | Profit 75 | 15% |
| 500 | 450 | Loss 50 | 10% |
| 800 | 880 | Profit 80 | 10% |
| 800 | 740 | Loss 60 | 7.5% |
| 600 | 636 | Profit 36 | 6% |
Invented teaching prices. The percentage column uses each row’s cost, not its selling price. Check 60/800 × 100 = 7.5% in row four.
Compare the same quantity and include the stated related expenses in cost.
G = S − C (when S > C) L = C − S (when S < C) Profit % = 100G/C; loss % = 100L/C
A percentage is a ratio per hundred, not a taka amount. Cost zero makes this percentage undefined.
Each percentage applies to that seller’s own cost.
At profit: S = C(1 + q), C = S/(1 + q) At loss: S = C(1 − q), C = S/(1 − q) Final = initial × (1 + q1)(1 + q2)
The inverse loss formula requires q < 1 here. Multiplying the rates’ factors preserves their different bases.
Convert every group price to cost per piece, then use the actual quantities.
| Buying plan | Pieces | Total cost (Tk) | Mean cost/piece (Tk) |
|---|---|---|---|
| 12 pieces at 8 per 24 | 12 | 36 | 3 |
| 12 pieces at 12 per 24 | 12 | 24 | 2 |
| Equal pieces combined | 24 | 60 | 2.50 |
| Spend 24 at each price | 8 + 12 = 20 | 48 | 2.40 |
Invented data. Equal-piece cost is 60/24; equal-spending cost is 48/20. Selling at 2.50 per piece breaks even only for the first combined plan.
Match each letter to its explanation. Read the quantities, units and relationships, then check the counts or equations. These are original teaching models.
Original invented prices; one drawing unit represents Tk 2. This is a comparison model, not a current price chart.
Match each letter to its explanation. Read the quantities, units and relationships, then check the counts or equations. These are original teaching models.
Original invented values. Box sizes do not encode money amounts; numeric labels and arrow multipliers carry the relationship.
Show your working on paper. Check your answer, then choose Next.
500
480 + 20 = 500.
75
575 − 500 = 75.
50
500 − 450 = 50.
15
100 × 75/500 = 15; write 15, not the decimal rate 0.15.
10
100 × 50/500 = 10.
neither
Their difference is zero.
600
690/1.15 = 600; check 600 + 90 = 690.
560
640 × 0.875 = 560.
800
720/0.90 = 800.
800
The difference is 25% of cost; 200/0.25 = 800.
20
Unit cost 5 and sale 6 give 100 × 1/5 = 20.
neither
Mean unit cost and selling price are both Tk 2.50.
1320
1000 × 1.20 × 1.10 = 1320.
1300
1716/(1.10 × 1.20) = 1300.
5
100 × 46/920 = 5.
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Stated related expenses belong to the full cost. A Tk 480 purchase plus Tk 20 transport costs Tk 500; selling for Tk 575 gains Tk 75, not Tk 95.
Identify included expenses and compare the same quantity.
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Mark cost 500 as 100%, an added 75 as 15%, and selling price 575 as 115% of cost. The 15% is based on cost.
Check labels, proportions and the named base.
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The rows give profit 80 at 10%; loss 60 at 7.5%; and cost 600 with profit 36 at 6%. Each percentage divides the change by its own cost.
Require all four quantities and calculation steps.
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The numerator is right but the denominator is selling price. Profit on cost is 75/500 × 100 = 15%. The other ratio uses a different base.
Do not claim the other arithmetic is impossible; identify what it measures.
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Profit = 720 × 0.125 = 90; sale = 810. Reverse: 810/1.125 = 720.
Check both routes and taka units.
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Cost = 765/0.85 = 900. Adding 15% of 765 uses sale as the base and gives 879.75, not the original cost.
Show the correct multiplier and reverse check.
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0.15C = 120, so C = 800. Prices are 760 and 880, differing by 120.
Both rates must use the same cost.
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Three quads are twelve items; cost 84, sale 96, profit 12. Percentage = 100 × 12/84 = 100/7%, about 14.29%.
Use exact fractions until the final stated rounding.
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First unit cost is 4, so 100 cost 400. The two batches cost 96 + 72 = 168 and all 48 sell for 192, giving profit 24 and rate 100/7%, about 14.29%. Mean cost is 3.50; four pieces for 25% profit must sell for 4 × 3.50 × 1.25 = 17.50.
Check equal quantities, the requested quantity and all percentage bases.
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Fourteen items cost 48 and sell for 56. Profit = 8; percentage = 100/6%, about 16.67%. Equal spending differs from equal pieces.
Check quantities and do not reuse the equal-piece mean.
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The first sale is 600 and the next is 720. Profit relative to 500 is 220, or 44%. The second 20% is calculated on 600.
A claim of 40% must be corrected with both stages.
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Initial cost = 1584/1.20/1.10 = 1200. Intermediate sale = 1320. Check 1320 × 1.20 = 1584.
Name which price is each seller’s cost.
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No. A cost 1000 becomes 900 and then 990. The final price is 1% below the first cost because the bases differ.
Use multipliers or a valid numerical counterexample.
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Loss = 90 and sale = 1110. Check 1110 + 90 = 1200 and 90/1200 = 0.075.
Require units and the correct base.
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For example (400,500) and (800,1000). Each sale is 1.25 times cost even though the profit amounts are 100 and 200.
Accept other valid positive pairs after checking their ratios.
Create a miniature shop ledger with one profit, one loss, one no-change row and a two-seller chain.
Keep your work on paper or in a local file. This page does not upload it or automatically grade the project.
This original Kidemy practice follows the topic order of 2026 Class 8 Mathematics · English Version, chapter 2, printed pages 12–28. It does not replace the complete chapter or its practical teaching.
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