In 1986 the book value of a certain car was 2/3 original

Question

In 1986 the book value of a certain car was 2/3 original price, and in 1988 its book value was 1/2 the original purchase price. By what percent did the book value for this car decrease from 1986 to 1988?

(A) 16 2/3%
(B) 25%
(C) 33 1/3
(D) 50%
(E) 75%

(A) 16 2/3%
(B) 25%
(C) 33 1/3
(D) 50% 
(E) 75%

Bunuel · Accepted Answer

General formula for percent increase or decrease, (percent change):  percent=\frac{Change}{Original}*100 .

Say the original price was $6, then:
In 1986 the book value of the car was 2/3*6=$4;
In 1988 the book value of the car was 1/2*6=$3;

Hence from 1986 to 1988 the book value for this car decreased by  percent=\frac{Change}{Original}*100=\frac{4-3}{4}*100=25% .

Answer: B.

JustinDragna · Answer

i can see it if i draw it, but i cannot for some reason solve it arithmetically. i feel like it should be easy, but I can't see it.

JustinDragna · Answer

Ok, that makes sense. If you have 4 and then go to 3, that's going to be a 25$ decrease from the original value of 4.

I thought the question was asking the percent it decreased from the original price between 1986 and 1988, which would just be the difference between the two fractions *100, or 1/6(100).

Now, that I look back at my original drawing, it doesn't even make sense the way i was thinking about it.

Anyway, thanks for the help.

ziko · Answer

Let say the original price of a car is 30 000 $, in 1986 its price is 20 000 $ (2/3 of 30000), in 1988 its value is 15 000$ (1/2 of 30000). The change in price between 86 and 88 is 5000, 5000 is 25% of 20000 (we need to take 20000 because we calculate the change from this year).

JusTLucK04 · Answer

Best numbers: 300- Original

In 1986- 200
In 1988- 150

Decrease of 50 over 200 between 86 and 88
So 25%

pinkcupcake · Answer

Thanks this is very helpful - quick question though, i see the percentage change formula is change/originalx100.. shouldn't the original be $6 dollars instead of 4 dollars?

KarishmaB · Answer

Original means "base value" or the "reference value"

"By what percent did the book value for this car decrease from 1986 to 1988"
means that as compared with the value in 1986, by what percent did the value decrease in 1988?

So the base value is the 1986 value which is 4.

PareshGmat · Answer

Let the original value = 1

Change  = \frac{1}{2} * 100 * \frac{3}{2} = 75

Percent change = 100-75 = 25%

saswata4s · Answer

Suppose, the price was $300

in 1986 book value = 2/3 of $300 = $200
in 1988 book value = 1/2 of $300 = $150

Change in book value = $50
percentage change of book value= (50/200) * 100 = 25%

Ans: B.

shashankism · Answer

Lets say original value be x 
in 1986 book value = 2/3x
In 1988 book value = 1/2x
Change from 1986 to 1988 = 2/3x - 1/2 x = 1/6 x
Percentage change from 1986 to 1988 =  *100 = 25%

Answer B

shashankism · Answer

Alternatively since the LCM of 3 and 2 is 6 . So lets take original price as some multiple of 6, say 60
Original price = 60
In 1986, book value = 2/3*60 = 40 
In 1988 book value = 1/2*60 = 30 
Percentage change from 1986 to 1988 = (40-30)/40 * 100 = 25%

Answer B

We can solve by either method.. Taking a value will help us to solve this question in a faster manner.

Rahulbasu007 · Answer

The easiest approach, I think, is to simply consider a nice number.

Let, the original price = 12

Initial book value = 2/3 * 12 = 8
Final book value = 1/2 * 12 = 6

Difference = 8-6 = 2
Percentage change = (change/original)*100 = (2/8)*100 = 25%

I was revisiting old questions where I made mistakes looong back, and thought that I'd post an explanation now.

I did a silly calculation mistake that time, by taking the original price as 100x. (Sometimes, it's so easy if you just plug in nice numbers!)

bumpbot · Answer

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In 1986 the book value of a certain car was 2/3 original

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