Grade 9 Percentages: Short Notes

9 ශ්‍රේණිය · 5 පරිච්ඡේදය · ප්‍රතිශත

100%

of Grade 9 term tests include it (40 of 40)

448

marks in past papers (86 questions)

10 min

full lesson with quick checks

🎯 What you'll learn

Find a percentage of an amount and write one amount as a percentage of another
Find profit or loss and the profit or loss percentage on the cost price
Find the selling price for a given profit percentage, and work back to the cost price
Use marked price, discount and commission in calculations
Compare deals to decide which gives more profit

Avurudu sale!

Before Avurudu, one shop in Nugegoda shouts '20% OFF!' while the shop next door says 'Rs. 1000 off every frock!'. Which is the better deal? And how does the shop still make a profit? Percentages answer both, in a few lines.

Percent means 'out of 100'

15% = 15/100 = 0.15.• x% of an amount: x/100 × amount. 15% of Rs. 2400 = 15/100 × 2400 = Rs. 360.• A as a percentage of B: A/B × 100%. Rs. 300 out of Rs. 1200 = 300/1200 × 100% = 25%.

Profit and loss

Cost price (CP): what the seller paid.Selling price (SP): what the seller gets.• SP > CP: profit = SP − CP• SP < CP: loss = CP − SPProfit and loss percentages are always worked out on the cost price.

🧮 Profit or loss percentage

P% = profit percentage, L% = loss percentage, SP = selling price, CP = cost price. Divide by the cost price, never by the selling price.

P% = (SP − CP)/CP × 100% L% = (CP − SP)/CP × 100%

✏️ A coconut trader in Kurunegala

A trader buys 200 coconuts at Rs. 60 each and sells them all at Rs. 75 each. Find his profit and profit percentage.

1CP = 200 × 60 = Rs. 12 000. SP = 200 × 75 = Rs. 15 000.
2Profit = 15 000 − 12 000 = Rs. 3000.
3Profit % = 3000/12 000 × 100% = 25%.

✅ Rs. 3000, 25%

✏️ Selling for a target profit

A rice cooker costs a shop Rs. 2400. The owner wants a 15% profit. What should the selling price be?

1Profit = 15/100 × 2400 = Rs. 360.
2SP = 2400 + 360 = Rs. 2760.
3Quicker: SP = 115% of CP = 1.15 × 2400 = Rs. 2760.

✅ Rs. 2760

⚠️ Don't take 15% off the selling price

For the bicycle, many students do 34 500 − 15% of 34 500 = Rs. 29 325. Wrong: the 15% was a percentage of the cost, not of the selling price. Check: 15% of 29 325 added back gives 33 723.75, not 34 500. In one O/L paper only 5% reversed a percentage like this. Always set the original amount as 100%.

Marked price and discount

The marked price is the price on the label. A discount is the amount taken off it.• Discount % is a percentage of the marked price.• Price paid = marked price − discount.A 20% discount means you pay 80% of the marked price.

⚠️ Which price is the 100%?

Each percentage has its own base:• Profit or loss % → on the cost price• Discount % → on the marked price• Commission % → on the sale priceDividing by the wrong price is the quickest way to lose marks. Before you divide, say which price is 100%.

📌 Remember

• x% of A = x/100 × A; A as a % of B = A/B × 100%.• Profit or loss % is on the cost price.• For a 15% profit, SP = 115% of CP; to go back, divide by 115 and multiply by 100.• Discount % is on the marked price; commission % is on the sale price.• Percentages taken one after another can't simply be added or subtracted.

🧾 Quick revision sheet

Profit	Selling price − cost price
Profit percentage	Profit ÷ cost price × 100%
Discount percentage is calculated on…	the marked price
After a 20% discount you pay…	80% of the marked price
SP for a 10% profit	1.10 × cost price
Cost price when SP = Rs. 1150 at 15% profit	1150 ÷ 115 × 100 = Rs. 1000
Commission	A percentage of the sale price paid to the agent or broker.