How would I work out this question?

At a store, they cut the price 40% for a particular item. By what percent must the item be increased if you wanted to sell it at the original price?





(It's so I can practice for an aptitude test but not sure how I would work it out).How would I work out this question?
= (100%[1/{1 - 0.4}]) - 100%


= (100%[1/{0.6}]) - 100%


= (100%[5/3]) - 100%


= 500/3% - 100%


= 500/3% - 300/3%


= 200/3% or 66 2/3%





Answer: 66 2/3% or 2/3





Proof:


An item was offered for sale at $100.00 then was reduced by 40% for a new discounted price of $60.00.





To restore it to it's original $100.00:


= $60.00 + 66 2/3%($60.00)


= $60.00 + 2/3($60.00)


= $60.00 + $40.00


= $100.00





Or simply:


= (1 + 2/3)($60.00)


= 1 2/3($60.00)


= 5/3($60.00)


= $300.00/3 or $100.00How would I work out this question?
Using actual numbers helps. Say the item is $100 since the question is using percentages. If it is cut by 40%, which is $40, the item now costs $60. In order for the item to be back at its original $100, the $40 taken away from it have to be added back, but this time the $40 is out of $60. So the percentage the item must be increased by to sell it at its original price is 40/60 = 2/3 = about 66.667% or 66 and 2/3%.





ANSWER: 66 and 2/3%
Use the proportions percent over 100 %26amp; part over whole





40.(known) Sale price ( unknown)


------------ equals --------------


100. Original price ( known)





Do cross products (40 times the original price divided by 100)





Now you have the Amunt of discount in dollars, subtract that from the original price to get sale price





Use the same proportions again to find the percent needed to get back to 100. ( u just have different known and unknowns)





Sale price (known). Percent ( unknown)


----------------------- equals -------------------------


Original price (known). 100





Cross products, sale price times 100 divided by the original price
Lets say the item costs $10.50 to start with and the store cuts the price by 40%.


10.50 x .4 = 4.20


10.50 - 4.20 = $6.30


To find the percentage to increase the sale price to get back to the original price, divide the orginal price by the sale price.


10.50/6.30 = 1.666667


Multiply the sale price by the resulting percentage and you will get back to the original price.


6.30 * 1.6666667 = 10.50
Because you multiplied the original price by 0.6 to get the discounted price, you must divide by 0.6 to get the original price. Dividing by 0.6 is the same as multiplying by 1/0.6 = 5/3 = 1.6667.





Since we only want to know what percent increase is required, drop the 1, and the answer is 0.6667 = 66.67%
If original price is $ 100,





the present price is 100 - 40 = $ 60





Price has to be increased from 60 to 100 i.e by 40 dollars





for 60 dollars hike is ------40 dollars





for 100 ------(40/60)100 = 200/3 = 66.67%
Say its 100 dollars. At 40% less it would be 100 x .6 = 60


so to bring it back to full price set up an inequality 60 x P = 100


then solve for P it will be a number over 1


in this case its 1.666


or 166.66%
To sell it at original price, you must use current price to divide 60%.





e.g. USD 12 / 0.60 = USD 20.





USD 20 * 60% = USD 12.
66.67%