Percentage and ratio practice

Part, whole and rate

A rate of $1$ is $100\%$. For example, $35\%$ of $240$ is $240 \times 0.35 = 84$, and $84$ as a percentage of $240$ is $84 \div 240 = 0.35 = 35\%$.

Discounts and profit

"$x\%$ off" means you pay $(100 - x)\%$ of the price: $20\%$ off $1800$ yen is $1800 \times 0.8 = 1440$ yen.

• list price = cost × (1 + markup)
• selling price = list price × (1 − discount)
• profit = selling price − cost

Salt-solution concentration

In mixing, diluting and evaporating problems, track the amount of salt: adding or removing water does not change it.

Example: $400$ g of a $20\%$ solution contains $80$ g of salt. To make it $4\%$, the total must be $80 \div 0.04 = 2000$ g, so add $1600$ g of water.