Question

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

Answer 1

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

Answer 2

The actual percentage of reduction is 52%

The first reduction is given as:

$r_1 = 40\%$

The second reduction is given as:

$r_2 = 20\%$

Assume that the original price of the item is x.

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

$New = x\times (1 -r_1)$

So, we have:

$New = x\times (1 -40\%)$

$New = x\times 0.6$

$New = 0.6x$

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

$New = 0.6x\times (1 -r_2)$

So, we have:

$New = 0.6x\times (1 -20\%)$

$New = 0.6x\times 0.8$

$New = 0.48x$

Recall that the original price is x.

So, the actual reduction is:

$Actual = \frac{x - 0.48x}{x}$

$Actual = \frac{0.52x}{x}$

Divide

$Actual = 0.52$

Express as percentage

$Actual = 52\%$

Hence, the actual percentage of reduction is 52%

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