Calculating percentages

Percentages are a useful way of showing how different parts of the same thing relate to each other. For example, the products from the chemical industry can be divided into six different categories as shown in the pie chart by value of sales. Output ranges widely from those produced in huge quantities (millions of tonnes) to chemicals produced in kilogram quantities but with very high values.

If the overall value of the industry is known, then from the percentages given it is possible to determine how much each sector is worth.

Profits and losses are often expressed as percentages. This information may then be used to help predict future productivity in terms of both expansion and or contraction of different parts of the industry. Therefore, it is important to know how to carry out calculations involving both percentage increases and percentage decreases. Being able to work out and use multipliers, is the key to success here!Multipliers are worked out from the ratio of the % change, ie,

For example:

  • for an increase of 12% (or 12% profit), the multiplier = \inline \dpi{100} \frac{112}{100} = 1.12 
  • for an decrease of 12% (or 12% loss), the multiplier = \inline \dpi{100} \frac{88}{100} = 0.88 

Worked example 1

The cost of the reactants increased by 15%. The new price was £122, what was the old price?

The multiplier = \inline \dpi{100} \frac{115}{100} = 1.15

Therefore, the old price is £122 ÷ 1.15 = £106 

Worked example 2

The local supplier announced that all raw materials were to increase by 6.2% in the new year. If a factory currently pays £150,000 for the raw materials, what will the new price be?

The mutliplier is  \inline \dpi{100} \frac{106.2}{100} = 1.062.   So the new price will be £150,000 x 1.062 = £159,300

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