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Price of an item is reduced by 40% of its original price. A week later it’s reduced 20% of the reduced price. What’s the actual % of the reduction from the original price

Respuesta :

gilbertazavedo72

Answer: 52%

Step-by-step explanation:

Let the original price be 100.

After 40% reduction, price will be 100 - 40% = 60

After further 20% reduction, price will be 60 - 20% = 48

%age = (cur val - orig. val ) / orig val x 100

= (48 - 100) / 100 x 100%

= -52

MrRoyal

The actual percentage of reduction is 52%

The first reduction is given as:

[tex]r_1 = 40\%[/tex]

The second reduction is given as:

[tex]r_2 = 20\%[/tex]

Assume that the original price of the item is x.

After the first reduction of 40%, the new price would be:

[tex]New = x\times (1 -r_1)[/tex]

So, we have:

[tex]New = x\times (1 -40\%)[/tex]

[tex]New = x\times 0.6[/tex]

[tex]New = 0.6x[/tex]

After the second reduction of 20% on the reduced price, the new price would be:

[tex]New = 0.6x\times (1 -r_2)[/tex]

So, we have:

[tex]New = 0.6x\times (1 -20\%)[/tex]

[tex]New = 0.6x\times 0.8[/tex]

[tex]New = 0.48x[/tex]

Recall that the original price is x.

So, the actual reduction is:

[tex]Actual = \frac{x - 0.48x}{x}[/tex]

[tex]Actual = \frac{0.52x}{x}[/tex]

Divide

[tex]Actual = 0.52[/tex]

Express as percentage

[tex]Actual = 52\%[/tex]

Hence, the actual percentage of reduction is 52%

Read more about percentage change at:

https://brainly.com/question/809966

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