An auto dealer sells each car at either $20,000 or $30,000. Some cars

Question

An auto dealer sells each car at either $20,000 or $30,000. Some cars are marked up at 20% of the cost price and the remaining are marked up at 30% of the cost price. If the dealer sells 50 cars in total, what is the total profit of the dealer?

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Official Answer

E

souvonik2k · Answer

Though i got the answer wrong.
After further analysis, I observed that:
S1 does not state whether the 20 cars were marked up 20% or 30%.
Also, as per the question, the C.P. is not given, hence cars of 20,000 or 30,000 can have marked up of 20% or 30%.
S2 again does not give this information.
Hence IMO E.

Correct me if i am wrong.

rajeshkpandey · Answer

Key points
Each cars sold at either $20,000 or $30,000.
Total cars the dealer sells 50.
To find- total profit
Revenue from the cars sold at $20,000 + Revenue from the cars sold at $30,000.

St-1: 20 cars were sold for $20,000
Good that 20 cars were sold at $20,000 but isn't $20,000 suppose to be a 20% or 30% marked up price of the cost price. And what is that cost price?? Cant find. And,therefore, Not sufficient!!

St-2: 30 cars were marked up 30%
It states that 30 cars were marked up 30%. That means the remaining 20 were marked at 20% of the cost price. But again, What is the cost price of the two batches of the cars sold? Data not sufficient

Combining statement 1 and 2, we get that
20 cars were sold at $20,000 and that 30 cars were marked up 30% or the remaining 20 were marked at 20% of the cost price.
let CPx - cost price of 20 cars
and CPy - cost price of 30 cars
now cost price of 1 car of 20 cars= 1.2*x=20000.
= x= 20000/1.2=5000/3
Therefore, 20 cars = (5000/3)*20= some value
SPx(selling price of 20 cars
)= 20*20000= 400000
profit from batch of 20 cars= 400000-[20*(5000/30] = some value
Similarly , for another batch of 30 cars profits can be known
Therefore combining gives a sufficient solution.

Please correct me if E is the correct option.

SSwami · Answer

An auto dealer sells each car at either $20,000 or $30,000. Some cars are marked up at 20% of the cost price and the remaining are marked up at 30% of the cost price. If the dealer sells 50 cars in total, what is the total profit of the dealer?
GIVEN: SP of each car is either $20,000 or $30,000
To be Calculated: Total profit on selling 50 cars

(1) 20 cars were sold for $20,000
but we do not know the marked-up %for these.
Therefore, not sufficient.

(2) 30 cars were marked up 30%
Therefore remaining 20 were marked up 20%
but we do not know the MP and hence cannot calculate the SP

Both: 20 cars were sold for $20,000 and 20 were marked up 20%
 Total SP = 20* 20,000 =400,000
1.2CP = 400,000
CP = 333,333

Similarly, 
30 cars were sold for $30,000 and were marked up 30%
Total SP = 30* 30,000 =900,000
1.3CP = 900,000
CP = 692,307

And thus profit can be calculated!

Why is ans option C not correct?

KanishkM · Answer

Hey  SSwami

IMO

The inline assumption went wrong here:
1) 20 were marked up 20%
This is a far fetched assumption, since the word some can be any number between 1 and 20, inclusive.

It could have been that 10 were marked up by 20% and the rest were sold at either $20,000 or $30,000.

They never mentioned that the split of marked up percentage's 20% and 30%, is done equally.

With that reason we will get different values for Profit.

Let me know if you think otherwise.

SSwami · Answer

Hi,
I am unable to understand the following 2 points:

1. The word "some" is not mentioned either in the question or in the statements.
2. The question clearly mentions "remaining are marked up at 30% of the cost price"
 which makes it clear that there are only 2 groups of cars- 
20%Marked up price and 30%Marked up price

KanishkM · Answer

SSwami , Kindly have a look here

An auto dealer sells each car at either $20,000 or $30,000.  Some cars  are marked up at 20% of the cost price and the remaining are marked up at 30% of the cost price. If the dealer sells 50 cars in total, what is the total profit of the dealer?

(1) 20 cars were sold for $20,000
(2) 30 cars were marked up 30%

Parvez786 · Answer

s1 : 20 cars for $20000 each , implies remaining 30 cars for $30000 each . but no Link with the second half of the que statement (some marked with 20% of CP , and remaining with 30% of CP ). we don't know how many marked with 20 % and how many with 30%. without that info ( no of cars with 30% ,and 20 % ) we cant calculate the total profit .
hence not sufficient

S2 : 30 cars were marked with 30% , means remaining 20 cars marked with 20 % . BUT what's are their respective prices ?? means they belong to SP of 30000 or 20000 . We don't know 
hence not sufficient

COMBINE S1 and S 2
SP : 20 cars for $20000 each , implies remaining 30 cars for $30000 each
AND
market price : 30 cars were marked with 30% , means remaining 20 cars marked with 20 %

but we don't know the connect between SP and market price .
means , if 20 cars SP is 20000 each they belong to which category (30% or 20%) .

hence both not suff
E ans

umangshah · Answer

An auto dealer sells each car at either $20,000 or $30,000. Some cars are marked up at 20% of the cost price and the remaining are marked up at 30% of the cost price. If the dealer sells 50 cars in total, what is the total profit of the dealer?

(1) 20 cars were sold for $20,000
(2) 30 cars were marked up 30%

Bunuel

Can you explain why Option C is not correct. 
Using Statement 1 we know 20 Cars were sold @ 20k and 30 Cars @30K
And Using Statement 2, we know 30 cars were sold @30% markup and remaining 20cars were sold @ 20% (Considering that question uses "either or " which means that there can be only two possibilities)

Now, combining both the statements would give us 20Cars@20K with 20% markup and 30cars@30k with 30% markup using which we can definitely calculate the profits.

Thanks

Bunuel · Answer

Option C is not correct because, even when combining both statements, we don't have a direct relationship between the price at which each car was sold and its respective markup.

From Statement 1, we know:

20 cars were sold at $20,000. 
  30 cars were sold at $30,000.

From Statement 2, we know:

20 cars had a markup of 20%. 
  30 cars had a markup of 30%.

However, we can't definitively say from the given information that the 20 cars sold for $20,000 all had the 20% markup, nor can we say that the 30 cars sold for $30,000 all had the 30% markup. It's entirely possible, for example, that some of the $20,000 cars had a 30% markup and some of the $30,000 cars had a 20% markup. Without this clarity, we can't accurately calculate the total profit. Thus, Option C, which implies combining both statements gives a definite answer, is incorrect.

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An auto dealer sells each car at either $20,000 or $30,000. Some cars

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