Ratio, Percentages and Money: notes

Ratio and Proportion

• Sharing in a ratio: add the parts, find one part, then multiply. Share $60 in the ratio 2 : 3. Parts = 5, one part = $12, shares are $24 and $36.
• Direct proportion: when one amount goes up, the other goes up in the same ratio. 3 books cost $12, so 5 books cost $20.
• Inverse proportion: when one goes up, the other goes down. 4 workers take 6 days, so 2 workers take 12 days.
• Speed: speed = distance / time. Distance = speed x time. Time = distance / speed.

Percentages

• Percentage of an amount: 15% of 80 = 0.15 x 80 = 12.
• Increase and decrease: increase by 20% means multiply by 1.2. Decrease by 20% means multiply by 0.8.
• Percentage change: change / original x 100. From $50 to $60 is 10 / 50 x 100 = 20%.
• Profit and loss: percentage profit = profit / cost price x 100. The base is always the original, here the cost price.

Money

• Simple interest: I = PRT / 100. $200 at 5% for 3 years gives 200 x 5 x 3 / 100 = $30.
• Compound interest: A = P(1 + R/100)^n. Interest is added each year and earns interest itself.
• Exchange rates: multiply to change into the other currency, divide to change back. Check which way the rate is quoted.
• Hire purchase: deposit plus all instalments. It costs more than the cash price.