the price of foodstuff generally increased by 20% at the beginning of a drought season and the new price reduced by 30% during har

1 thought on “the price of foodstuff generally increased by 20% at the beginning of a drought season and the new price reduced by 30% during har”

1. Answer:

   • Ratio between the new price and the original price is 21 : 25.

   Given that:

   • Price of food stuff increased by 20% at the beginning of a drought season.
   • The new price then reduced by 30% during harvesting season.

   To Find:

   • Ratio between new price and original price.

   Let us assume:

   • Original price of the food stuff be x.

   Price of the food stuff during drought season:

   x + (20% of x)

   [tex]\mathtt{\implies x +\bigg(\dfrac{20}{100}\times x\bigg)}[/tex]

   [tex]\mathtt{\implies x +\dfrac{20x}{100}}[/tex]

   [tex]\mathtt{\implies\dfrac{100x + 20x}{100}}[/tex]

   [tex]\mathtt{\implies\dfrac{120x}{100}}[/tex]

   [tex]\mathtt{\implies\dfrac{120x}{100}}[/tex]

   Price of food stuff during harvesting season:

   [tex]\mathtt{\dfrac{120x}{100}-(30\% \; of \; \dfrac{120x}{100})}[/tex]

   [tex]\implies\mathtt{\dfrac{120x}{100}-\bigg(\dfrac{3\!\!\!\not{0}}{10\!\!\!\not{0}}\times\dfrac{12\!\!\!\not{0}x}{10\!\!\!\not{0}}\bigg)}[/tex]

   [tex]\implies\mathtt{\dfrac{120x}{100}-\bigg(\dfrac{3}{5}\times\dfrac{6x}{10}\bigg)}[/tex]

   [tex]\implies\mathtt{\dfrac{120x}{100} – \dfrac{18x}{50}}[/tex]

   [tex]\implies\mathtt{\dfrac{120x-36x}{100}}[/tex]

   [tex]\implies\mathtt{\dfrac{84x}{100}}[/tex]

   Ratio between new price and original price:

   [tex]\implies\mathtt{\dfrac{84x}{100}\div x}[/tex]

   [tex]\implies\mathtt{\dfrac{84\!\!\!\not{x}}{100}\times\dfrac{1}{\not{x}}}[/tex]

   [tex]\implies\mathtt{\dfrac{84}{100}}[/tex]

   [tex]\implies\mathtt{\dfrac{84\div4}{100\div4}}[/tex]

   [tex]\implies\mathtt{\dfrac{21}{25}}[/tex]

   21 : 25

   Hence, the ratio between the new price and the original price is 21 : 25.

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