Flashcards · 13 cards

Commercial arithmetic

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Rule
How do you increase an amount by 15% in one step?
Answer
Multiply by $1.15$ . A decrease of 15% multiplies by $0.85$ .
Percentage changeIncrease: × (1 + r/100). Decrease: × (1 − r/100)
From the lesson: Percentages, profit and loss
Rule
A profit percentage is a percentage of what?
Answer
Of the cost price: $\dfrac{\text{selling price} - \text{cost price}}{\text{cost price}} \times 100\%$ .
Profit on the cost priceThe percentage is always of the cost price
From the lesson: Percentages, profit and loss
Know it
After a 30% rise a price is ₦1,040. How do you find the price before?
Answer
Divide by the multiplier: $1040 \div 1.3 = 800$ , so ₦800. Taking 30% off ₦1,040 gives the wrong answer.
From the lesson: Percentages, profit and loss
Rule
A discount is taken off which price?
Answer
The marked price.
DiscountTaken off the marked price
From the lesson: Percentages, profit and loss
Rule
A 40% cut and then a 30% cut: what is the total cut?
Answer
Multiply the multipliers: $0.6 \times 0.7 = 0.42$ . The price is 42% of the start, a 58% cut, not 70%.
Two changes in a rowMultiply the multipliers: 0.6 × 0.7 = 0.42
From the lesson: Percentages, profit and loss
Rule
The simple interest formula?
Answer
$I = \dfrac{PRT}{100}$ , with $T$ in years. The amount is $A = P + I$ .
Simple interestThe same interest every year: I = PRT/100
From the lesson: Interest, depreciation and growth
Rule
The compound interest formula?
Answer
$A = P\left(1 + \dfrac{r}{100}\right)^n$ , and the interest is $A - P$ .
Compound interestEach year × (1 + r/100), so the steps grow
From the lesson: Interest, depreciation and growth
Rule
The value after $n$ years of depreciation at $r\%$ a year?
Answer
$P\left(1 - \dfrac{r}{100}\right)^n$ : each year the value falls by $r\%$ of what it is worth then.
DepreciationEach year × (1 − r/100), so the value falls by less each year
From the lesson: Interest, depreciation and growth
Rule
Share ₦600 in the ratio 2 : 3.
Answer
Add the parts: $2 + 3 = 5$ . Then take each fraction of the total: $\frac25 \times 600 = 240$ and $\frac35 \times 600 = 360$ , so ₦240 and ₦360.
Sharing in a ratioAdd the ratio parts, then take each fraction of the total
From the lesson: Shares, tax, commission and exchange
Rule
Income tax: which part of the income is taxed?
Answer
Only the taxable income. Take every allowance off first, then use each tax band only up to its limit.
Income taxAllowances off first; tax only the taxable income
From the lesson: Shares, tax, commission and exchange
Rule
How many shares can you buy with ₦5,000 at ₦2.50 each?
Answer
Number of shares = money ÷ market price: $5000 \div 2.5 = 2000$ .
Shares and dividendsNumber of shares = money ÷ market price
From the lesson: Shares, tax, commission and exchange
Which method?
WAEC 2018 · Paper 2 · Q7 (a)
A shop had two reduction sales during which prices of all items were reduced by $40\%$ in the first sale and $30\%$ in the second. If a shirt was sold at GH₵ 35.00 during the second reduction sale, find the price before the first sale.
How do you undo the two reductions?
Answer
Together they multiply the price by $0.6 \times 0.7 = 0.42$ . So divide the sale price by 0.42.
From the lesson: Percentages, profit and loss Try the question
Which method?
WAEC 2022 · Paper 2 · Q7 (a)
A television set purchased for ₦65,000.00 depreciates by $14\%$ per year. Find the value of the television at the end of the third year.
Is 14% of the price paid taken off each year?
Answer
No: 14% of what it is worth at the start of each year. So multiply by 0.86 three times: $65\,000 \times 0.86^3$ .
From the lesson: Interest, depreciation and growth Try the question