A shop owner raises the price of a $150 pair of shoes by 40%. After few weeks because of falling sales the owner reduced the price of shoes by 40%
What is the mistaken assumption
The mistaken assumption is that reducing the price by 40% after increasing it by 40% would bring the price back to $150, which is not the case. The price would actually be lower than $150 because a 40% increase and a 40% decrease are not equal and opposite. To get back to the original price, the shop owner would need to reduce the price by 37.5%.
150 increased by 40%
To find the price after increasing by 40%, we can calculate 40% of $150 and add it to $150:
40% of $150 = 0.4 x $150 = $60
Price after increasing by 40% = $150 + $60 = $210
Therefore, the new price of the shoes is $210 after the increase.
$210 what percentage would have to be decreased back to $150
To find out what percentage the price of $210 would have to be decreased by to get back to the original price of $150, we can use the following formula:
% decrease = (amount of decrease ÷ original price) x 100%
We need to find the amount of decrease required to go from $210 to $150. This is:
$210 - $150 = $60
Now we can substitute this into the formula:
% decrease = ($60 ÷ $210) x 100%
% decrease = 28.57%
Therefore, the price of $210 would have to be decreased by 28.57% to get back to the original price of $150.
Annual number of burglaries in a town rose by 50% in 2012 and fell by 10% in 2013. Hence total of burglaries increased 40% over 2 year period.
What is the mistaken assumption
The mistaken assumption is that the percentage increase and decrease in the number of burglaries can be simply added or subtracted to get the total percentage change over two years.
For example, if there were 100 burglaries in 2011, a 50% increase would bring the number to 150 burglaries in 2012. If there were a 10% decrease in 2013, it would bring the number down to 135 burglaries. But this does not mean that the total percentage change over the two years is 40%.
To find the actual percentage change, we need to take into account the fact that the percentage increase and decrease in the second year apply to a different base number than the first year. Therefore, we need to use compound interest formula to calculate the actual percentage change.
Using the compound interest formula:
A = P(1 + r1/100)(1 + r2/100)
where A is the final number of burglaries, P is the initial number of burglaries, r1 is the percentage increase in the first year, and r2 is the percentage decrease in the second year.
In this case, we can plug in the values:
A = P(1 + 50/100)(1 - 10/100)
A = P(1.5)(0.9)
A = 1.35P
Therefore, the actual total percentage change over the two-year period is:
(1.35P - P) / P x 100%
= 0.35P / P x 100%
= 35%
So, the actual percentage increase in burglaries over the two-year period is 35%, not 40%.
Annual number of burglaries in a town rose by 50% in 2012 and fell by 10% in 2013. Hence total of burglaries increased 40% over 2 year period.
By what percentage would crime have to decrease for the 2 year to 40% increase
To find out what percentage the number of burglaries would have to decrease by for the total over the two-year period to be a 40% increase, we can use the following formula:
(1 + x/100) * (1 - 10/100) * (1 + 50/100) = 1 + 40/100
where x is the percentage decrease we need to find.
Simplifying this equation:
(1 + x/100) * 0.9 * 1.5 = 1.4
1.35 * (1 + x/100) = 1.4
1 + x/100 = 1.4/1.35
1 + x/100 = 1.037
x/100 = 0.037
x = 3.7
Therefore, the number of burglaries in the town would need to decrease by 3.7% over the two-year period for the total to be a 40% increase.
A store currently offering 60% discount on all items purchased. Cashier trying to convince to open a credit card and receive an additional 20% off that means your getting 80% off
What is the mistaken assumption
The mistaken assumption is that the additional 20% discount obtained by opening a credit card is being calculated as a percentage of the original price before the 60% discount.
In reality, the additional 20% discount should be calculated as a percentage of the price after the 60% discount has already been applied. By offering a 20% discount on the already discounted price, the store is effectively offering a discount of:
100% - 60% = 40%
On this already discounted price, the additional 20% discount offered for opening a credit card would represent a further reduction of 20% of the remaining 40%. Therefore, the total discount would be:
60% + (20% of 40%) = 60% + 8% = 68%
So, the total discount would be 68% and not 80% as the cashier has claimed.
A store currently offering 60% discount on all items purchased. Cashier trying to convince to open a credit card and receive an additional 20% off
Is it better to apply the 60% discount first or the 20% discount
It is better to apply the 60% discount first and then the 20% discount. This is because if we apply the 20% discount first, the price will be reduced by 20% of the original price, which will be higher than if we apply the 60% discount first.
For example, let's say the original price of an item is $100. If we apply the 20% discount first, the price will be reduced to:
$100 x 0.8 = $80
If we then apply the 60% discount, the price will be further reduced to:
$80 x 0.4 = $32
However, if we apply the 60% discount first, the price will be reduced to:
$100 x 0.4 = $40
If we then apply the 20% discount, the final price will be:
$40 x 0.8 = $32
As we can see, the final price is the same in both cases, but by applying the 60% discount first, we get a higher initial discount and pay less tax (if applicable) on the discounted price.