An air-conditioning unit costs $470. On December there was a discount

Price after discount and again raising by 16%= 470 * 82/100 * 116/100

We don't really need to multiply the whole expression. The units digit of this expression will be '8' , and only option A has 8 as units digit.

Hence A is the answer

If a number N is decreased first by x% and increased next by y%, then the total percent change is : ( Successive discount )

(- x + y - x y/100)%

Here X = 16 % decrease , Y = +16 % increase

=> -16 + 16 - 16 * 16 /100.
=> - 2.56 => - 2.5 ( approx)

Now - 2.5 % ( 470 )
=> - 25/1000 ( 470 )
=> - 11.75 => - 12 ( approx) -> discount

So, there is 12 $ decrease in the actual 470 => 458..Choice A.

Logically also if u see then the discounted price is much greater than the raised price ...so any option lesser than actual price will be the most probable contender

Here in this case only one value..ie 458 exists

thus Ans A

Original price: $470

During holiday
16% of 470 is 75.2
So the discounted price was = 470-75.2= 394.8

After holiday:
Price it hiked by 16% from the current price 394.8
so 16% of 394.8 = 63.168

So the price is = 394.8+63.168 = 457.9 = 458

Answer is A

Took me a while to do this manually.

I approached the problem this way: 470*0,84*1,16=470*0,9744 is less than 470=> A (458$)

An air-conditioning unit costs $470. On December there was a discount for Christmas of 16%. Six months later, the holiday season was over so the company raised the price of the air-conditioning by 16%. How much will an air-conditioning unit cost in November?
A. $458
B. $470
C. $472
D. $484
E. $491

Cost of AC = $470
On Christmas discount of 16% = 84% of 470 = \(\frac{84}{100}\) x 470 = $394.8
After six months price raised by 16% = 116% of 394.8 = \(\frac{116}{100}\) x 394.8 = 457.968 = (Approximately) = $ 458
Answer A...

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Whenever we increase a number by x%, then decrease it by x% (OR first decrease it by x%, then increase it by x%),
there is always a Net decrease, which is given by (x^2)/100 %

So the price of air conditioning unit will decrease overall by 16^2/100 % OR 2.56%

But even if we don't do this calculation here, we know that final price has to be less than initial price of $470.
So required answer must be < 470

Only one option, Option A. Answer is A

This can be solved without calculation:

Hence, Option A.

Explanation:
Logic : if we reduce the item price first and the increase the price of same item than the result is reduced price.

For example: Let the CP of an article be = 100
reduce = 10% = 90 (new price after decrease)
Increase = 10% (99 new price after increase )

Result = 100 - 99 = 1 % less.

Therefore answer will be less than $470. There is only one option (A).

Effective percentage increase/decrease is \(+16 - 16 -\frac{16*16}{100} = -2.56\)%

So, The price of the AC unit is 100 \(- \frac{2.56}{100}*470 ~ 458\)

Thus, the correct answer must be $ 458

Hence, the answer must be (A) 458

We can create the following expression:

(470)(0.84)(1.16)

= (470)(84/100)(116/100)

= (470)(21/25)(29/25)

= (94)(21/5)(29/25)

≈ 458

Alternate solution:

We should know that given a positive value, if this value is decreased by p percent and later increased by p percent (i.e., the same percentage), the new value will be always less than the original value. For example, let’s say we decrease the number 100 by 10 percent and then increase the result by 10 percent, the new value is 100 x 0.9 x 1.1 = 90 x 1.1 = 99, which is less than the original value of 100.

Since in this problem we decrease 470 by the same percentage (16%) as we increase it, the new number should be less than 470. Since the only number in the given answer choices less than 470 is 458, 458 is the correct answer.

Answer: A

Net % change is \(-16 + 16 +\frac{(-16)(16)}{100}=-2.56\)

So, Final cost will be \(\frac{(100 - 2.56)*470}{100}\) ~ \(458\), Answer must be (A)