Grade 10 Percentages: Short Notes

10 ශ්‍රේණිය · 2 වාරය · 13 පරිච්ඡේදය · ප්‍රතිශත

85%

of Grade 10 term tests include it (46 of 54)

840

marks in past papers (127 questions)

12 min

full lesson with quick checks

🎯 What you'll learn

Find annual and quarterly rates, and work back to the assessed value
Find customs duty and VAT, forwards and backwards
Calculate income tax using a tax-free allowance and tax slabs
Use I = P × r × t / 100 to find interest, principal, rate or time
Compare loans and deposits by calculating the interest, and choose the better one

Percentages at home

Thaththa pays rates to the Pradeshiya Sabha every quarter. The electricity bill has VAT added. Akka is choosing between two loans for a three-wheeler. Every one of these is a percentage question, and getting them right can save your family thousands of rupees.

Three moves with percentages

r% of A = A × r/100Add r% (duty, VAT, interest): new amount = A × (100 + r)/100Work back from an amount B that already includes r%:original = B × 100/(100 + r)Example: 20% of Rs. 3000 = Rs. 600, so 3000 + 20% = Rs. 3600, and 3600 × 100/120 = Rs. 3000 again.

Rates

A local council (Municipal Council, Urban Council or Pradeshiya Sabha) gives each property an annual assessed value. The owner pays a percentage of it every year as rates.Annual rates = assessed value × rate%Rates are usually paid in 4 quarters (a quarter = 3 months):Quarterly rates = annual rates ÷ 4

✏️ Rates on a house in Kurunegala

The annual assessed value of a house is Rs. 48 000 and the council charges rates of 8%. Find (i) the annual rates (ii) the amount paid each quarter.

1Annual rates = 48 000 × 8/100 = Rs. 3840
2A year has 4 quarters, so divide by 4.
3Quarterly rates = 3840 ÷ 4 = Rs. 960

✅ (i) Rs. 3840 (ii) Rs. 960

Customs duty and VAT

Customs duty is a tax on goods brought into Sri Lanka. It is a percentage of the value of the imported goods.VAT (value added tax) is added to the price of goods and services, such as a phone or electricity bill.Both are found the same way: tax = value × r/100, and the total = value + tax.

✏️ Importing a phone

(i) A phone worth Rs. 45 000 is imported. Customs duty is 20%. Find its value after duty.(ii) A trader paid Rs. 6000 as customs duty at 12% on some goods. Find the value of the goods.

1(i) Duty = 45 000 × 20/100 = Rs. 9000
2Value after duty = 45 000 + 9000 = Rs. 54 000
3(ii) 12% of the value is Rs. 6000, so 1% is 6000 ÷ 12 = Rs. 500.
4100% = 500 × 100 = Rs. 50 000

✅ (i) Rs. 54 000 (ii) Rs. 50 000

⚠️ Taking the tax off the wrong amount

A bill of Rs. 5900 includes 18% VAT. What was the price before VAT?✗ 5900 − 18% of 5900 = Rs. 4838✓ 5900 is 118% of the price, so price = 5900 × 100/118 = Rs. 5000The tax was a percentage of the smaller, original amount, so work back with 100/(100 + r).

Income tax in slabs

Income tax is charged on a person's annual income. A first part is tax-free. The rest (taxable income) is taxed in slabs, each slab at its own rate. For example:• first Rs. 1 200 000: free• next Rs. 500 000: 6%• next Rs. 500 000: 12%• the rest: 18%Fill the slabs in order, one at a time.

⚠️ Forgetting the tax-free part

In O/L papers many candidates applied the tax rate to the whole income. Always:1. Make the income annual (monthly × 12).2. Subtract the tax-free amount.3. Fill the slabs in order.Also, don't use one rate for everything: each slab has its own rate.

🧮 Simple interest

P = principal (the money borrowed or deposited), r = rate per year (%), t = time in years, I = interest, A = total to repay or receive. If the rate is per month, t must be in months.

I = P × r × t / 100 A = P + I

📌 Remember

• Rates = assessed value × r%; quarterly = annual ÷ 4.• Duty and VAT: tax = value × r/100. To remove a tax already included, × 100/(100 + r).• Income tax: make it annual, subtract the free part, fill slabs in order.• Simple interest: I = P × r × t/100; match t to the rate (years or months).• To decide, work out the actual rupees for each option.

🧾 Quick revision sheet

Annual rates	Annual assessed value × rates percentage
How many quarters in a year?	4 (each quarter is 3 months)
What is customs duty?	A tax on imported goods, charged as a percentage of their value
Price B already includes r% tax. Original price?	B × 100/(100 + r)
First step in an income tax question	Find the annual income and subtract the tax-free amount
Simple interest formula	I = P × r × t / 100
1% per month is what rate per year?	12% per year (simple interest)