Question

the price of foodstuff generally increased by 20% at the beginning of a drought season and the new price reduced by 30% during harvesting season Express the new price as a ratio of the original price in its lowest form ​

Answer 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)

$\mathtt{\implies x +\bigg(\dfrac{20}{100}\times x\bigg)}$

$\mathtt{\implies x +\dfrac{20x}{100}}$

$\mathtt{\implies\dfrac{100x + 20x}{100}}$

$\mathtt{\implies\dfrac{120x}{100}}$

$\mathtt{\implies\dfrac{120x}{100}}$

Price of food stuff during harvesting season:

$\mathtt{\dfrac{120x}{100}-(30\% \; of \; \dfrac{120x}{100})}$

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

$\implies\mathtt{\dfrac{120x}{100}-\bigg(\dfrac{3}{5}\times\dfrac{6x}{10}\bigg)}$

$\implies\mathtt{\dfrac{120x}{100} - \dfrac{18x}{50}}$

$\implies\mathtt{\dfrac{120x-36x}{100}}$

$\implies\mathtt{\dfrac{84x}{100}}$

Ratio between new price and original price:

$\implies\mathtt{\dfrac{84x}{100}\div x}$

$\implies\mathtt{\dfrac{84\!\!\!\not{x}}{100}\times\dfrac{1}{\not{x}}}$

$\implies\mathtt{\dfrac{84}{100}}$

$\implies\mathtt{\dfrac{84\div4}{100\div4}}$

$\implies\mathtt{\dfrac{21}{25}}$

21 : 25

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