Class 8 · English Version · Mathematics
2026 Class 8 Mathematics · English Version · Chapter 2 · Chapter companion part
Read a fictional statement, follow transaction timing and solve multi-stage profit problems with explicit assumptions.
Class 8 English Version: part D 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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A statement records an opening balance, dated descriptions, money in (credits), money out (debits) and a running balance. In the fictional table, start with 10000, add deposit 2000 and profit credit 300, then subtract withdrawal 1500 and fee 100. Closing balance is 10700. The 700 net increase is not all profit: deposits and withdrawals also changed the balance.
Closing = opening + credits − debits. Separate a new deposit from a profit credit; a withdrawal is not automatically a loss from an investment. The fictional statement credits 300 profit, but that alone does not establish an annual rate without the balance history, period and calculation terms. A fee reduces the displayed balance; do not silently omit it.
At 8% simple annual rate, a principal of 80000 earns 80000 × 0.08 × 3/12 = 1600 in the first three months. Four equal quarterly payouts total 6400 for a year if the principal stays 80000. If these payouts leave the account, they do not themselves earn compound profit there. A stated term of several years does not mean the first payout uses all those years.
For an invented loan of 5000 at 10% yearly, with 2000 repaid at each year end after interest: first add 500 to reach 5500, then subtract 2000 to leave 3500. Next year add 350 to reach 3850 and repay 2000, leaving 1850. Subtracting the repayment before charging that year’s interest gives a different model. Always state timing.
For equal one-year periods, 3000 at 10% earns 300, while 2000 at 5% earns 100. Total profit 400 on total principal 5000 gives 8%. The unweighted average 7.5% ignores the unequal principals. The 8% measures total one-year simple profit per 100 of combined initial principal; it is not a guaranteed future return.
For a shared simple rate r, two amounts satisfy total profit I = r(P1t1 + P2t2). With 2000 for two years and 3000 for three years, the weighted time-principal total is 4000 + 9000 = 13000 taka-years. If total profit is 1300, r = 0.10 = 10% annually. Do not add the years and apply that sum to all of the money.
Let x + y = 10000 and annual simple profit be 0.08x + 0.04y = 600. Substitute y = 10000 − x to get 0.04x + 400 = 600; x = 5000 and y = 5000. The source mixed-loan example uses one-year interest in its solution although the opening wording does not state that duration explicitly. Our version states one year and checks both equations.
Compound example 5 on printed 26 writes 61740 − 5600 but reports 5740. Its original principal is 56000, so the consistent subtraction is 61740 − 56000 = 5740; the printed subtraction has a missing zero. Check inputs, units, timing, operations and the final balance. A correct-looking final number does not make every intermediate step correct.
In the fictional statement, total money in is 2300 and total money out is 1600. The balance rises by 700, while the profit-credit row is only 300. Reconciliation explains the difference without inventing an annual rate.
The chapter names understanding bank statements as an outcome but does not supply a statement facsimile. Kidemy’s invented table teaches that outcome; it is not a real customer record or bank document.
The saved answer page 188 gives selected exercise results. We independently recompute our fresh tasks and retain missing-condition notes where the printed question cannot determine a unique answer.
In Exercise 2.1(19), the two unit costs are 36/12 = Tk 3 and 36/18 = Tk 2. Equal numbers of bananas make average cost (3 + 2)/2 = Tk 2.50 each. Sale at 36/15 = Tk 2.40 loses Tk 0.10 per banana, or 0.10/2.50 × 100 = 4% of cost. A total cash loss needs the quantity bought. For 25% profit, four bananas cost Tk 10 and should sell for Tk 12.50. Do not average the pieces-per-taka rates.
Invented classroom data, not a real bank statement. A dash means no entry, not missing balance data.
| Date / description | Credit (Tk) | Debit (Tk) | Balance (Tk) |
|---|---|---|---|
| 1 Jun · opening | — | — | 10000 |
| 2 Jun · new deposit | 2000 | — | 12000 |
| 30 Jun · profit credit | 300 | — | 12300 |
| 30 Jun · withdrawal | — | 1500 | 10800 |
| 30 Jun · fee | — | 100 | 10700 |
Read across each row in the displayed order. Total credits 2300 minus total debits 1600 gives net increase 700; only 300 is labelled profit. No annual rate can be inferred from this table alone.
Invented loan 5000 at 10% annually; repay 2000 at each year end after charging that year’s interest.
| Year | Opening (Tk) | Interest (Tk) | Before payment (Tk) | Payment (Tk) | Closing (Tk) |
|---|---|---|---|---|---|
| 1 | 5000 | 500 | 5500 | 2000 | 3500 |
| 2 | 3500 | 350 | 3850 | 2000 | 1850 |
Row two opens with row one’s closing debt. This arithmetic assumes no fees, new borrowing or other transactions. Check the stated order before calculating.
Invented one-year simple-profit contributions; both investments last exactly one year.
| Principal (Tk) | Annual rate | Year profit (Tk) |
|---|---|---|
| 3000 | 10% | 300 |
| 2000 | 5% | 100 |
| Total 5000 | Combined 8% | Total 400 |
The combined 8% means 400 simple profit on 5000 in this one-year example. It is not the unweighted 7.5% average and not a future-return promise.
Use the transaction order specified in the task.
Closing = opening + credits − debits Bk = B(k−1)(1 + r) − Dk
Account reconciliation and a loan recurrence describe different ledgers. A payment before interest requires a different ordering; stop and clarify an unstated schedule.
State time explicitly: the split-rate example below lasts one year.
Shared r = I/(P1t1 + P2t2) x + y = T r1x + r2y = I (one year)
Unequal periods require their own time factors. A split-rate task without a duration cannot automatically use the one-year equation.
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 loan example, not lending terms. Box sizes are schematic; all money amounts are explicitly labelled.
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 statement extension for the chapter’s fourth outcome. No customer data, real bank document or implied annual rate.
Show your working on paper. Check your answer, then choose Next.
300
Read the profit row, not the total net balance change.
10700
10000 + 2000 + 300 − 1500 − 100 = 10700.
5000
5320 − 400 + 80 = 5000.
1600
80000 × 0.08 × 0.25 = 1600.
6400
4 × 1600 = 6400; no reinvestment is assumed.
3500
5000 × 1.10 − 2000 = 3500.
1850
3500 × 1.10 − 2000 = 1850.
8
(300 + 100)/5000 × 100 = 8.
10
1300/(2000 × 2 + 3000 × 3) × 100 = 10.
5000
0.08x + 0.04(10000 − x) = 600 gives x = 5000.
5000
10000 − 5000 = 5000.
11025
10000 × 1.05² = 11025.
debit
The debit column records money out.
700
10700 − 10000 = 700; this need not equal profit.
3850
3500 × 1.10 = 3850, provided no other transactions or fees occur.
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Opening 10000 → deposit 12000 → profit credit 12300 → withdrawal 10800 → fee 10700. Credits total 2300 and debits total 1600.
Check each running balance, labels and the final reconciliation.
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It includes a 2000 deposit, a 300 profit credit, a 1500 withdrawal and a 100 fee. Net change is 700 but the labelled profit credit is 300.
Separate cash flows from earnings.
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A debit is outflow. Closing = 4000 − 500 + 200 = 3700.
Explain the direction of both entries.
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No. The calculation period, eligible balance history and account terms are also needed. A new deposit or withdrawal may change the relevant balance.
Do not invent a guaranteed rate from one credit.
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The first quarter is 0.25 year, so payout = 120000 × 0.06 × 0.25 = 1800. Five years describes the overall term, not this first payout period.
Keep annual rate and elapsed time distinct.
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Four withdrawn 200 payouts total 800, leaving principal 10000. Reinvestment at 2% quarterly gives 10000 × 1.02⁴ = 10824.3216, or 10824.32 rounded at the end.
Name the nominal-rate convention, final rounding and different cash flows.
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Year one: opening 5000, interest 500, prepayment 5500, repayment 2000, closing 3500. Year two: opening 3500, interest 350, prepayment 3850, repayment 2000, closing 1850.
Require the order and all balances, not only the final debt.
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The stated model gives 5000 × 1.10 − 2000 = 3500. Paying first would give (5000 − 2000) × 1.10 = 3300; it changes transaction timing.
Show both conditional results and use the specified one.
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Profits are 360 and 360. Combined 720 on 10000 gives 7.2%. It is weighted by principal, not the simple mean 7.5%.
State the equal one-year period and what 7.2% measures.
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r = 2080/(4000 × 2 + 6000 × 3) = 2080/26000 = 0.08, or 8%.
Check each loan’s profit and their sum.
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x + y = 20000 and 0.08x + 0.05y = 1300. Substitution gives 0.03x = 300, so x = 10000 and y = 10000; check 800 + 500.
Both the total principal and profit equations must hold.
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The split earns 1300 in one year. The all-at-6% simple alternative earns 1200 in one year. The separate two-year compound scenario gives amount 22472 and profit 2472. Periods differ, so these are calculations under different conditions, not a ranking of actual offers.
Label each time period and avoid comparing unlike amounts as identical offers.
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The consistent operation is 61740 − 56000 = 5740. Subtracting 5600 would instead give 56140. The printed intermediate subtraction is missing a zero.
Mention the printed error and verify both subtractions.
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For example, an amount and annual rate alone do not determine principal. Add a duration, specify simple or compound calculation, and state any transaction timing before solving.
Check that the repaired problem has enough information and a verified answer.
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Choose an opening balance, at least one credit and debit, label all amounts and dates, and check each balance. For example 3000 + 500 − 200 = 3300, not 3700.
Accept different invented data; require a reconciled correction and clear fictional label.
Create a fictional statement, a repayment ledger and a mixed-rate solution; exchange them for checking.
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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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