Need expert help with my solution

A car dealership sold two cars: the first car at a 10% profit and the second car at a 10% loss, which gave them an overall profit margin of 5% from these two sales. If the dealership's total profit was $1000, what was the sale price of each car?

voodoo_child wrote:A car dealership sold two cars: the first car at a 10% profit and the second car at a 10% loss, which gave them an overall profit margin of 5% from these two sales. If the dealership's total profit was $1000, what was the sale price of each car?

$5,000 and $1,000
$9,000 and $5,000
$11,000 and $9,000
$15,000 and $5,000
$20,000 and $10,000

OA - D

S1 = selling price of car1
S2 = selling price of car2

S1 = 1.1C1; S2=0.9C2 ......(i)

S1 + S2 = 1.05(C1+C2) ...(ii)

Profit = $1000 = (S1+S2) - (C1+C2) = (1/20)*(C1+C2).......(iii)
Therefore, C1+C2 = 20K ......(iv)

Now, I can also solve (i) and (ii):
1.1C1 + 0.9C2 = 1.05C1 + 1.05C2 => C1 = 3C2 .......(v)

Using (iv) and (v), C1=5K and C2 = 15K

S1 =5K(1.1) = 5.5K
S2 = 13.5K.

Something is wrong. Can someone please help me?

NB: I know another easy method to solve this by using backtrace. However, I am not sure what's wrong with above equations...Please help me

Shalabh's Quants wrote:

voodoo_child wrote:A car dealership sold two cars: the first car at a 10% profit and the second car at a 10% loss, which gave them an overall profit margin of 5% from these two sales. If the dealership's total profit was $1000, what was the sale price of each car?

$5,000 and $1,000
$9,000 and $5,000
$11,000 and $9,000
$15,000 and $5,000
$20,000 and $10,000

OA - D

S1 = selling price of car1
S2 = selling price of car2

S1 = 1.1C1; S2=0.9C2 ......(i)

S1 + S2 = 1.05(C1+C2) ...(ii)

Profit = $1000 = (S1+S2) - (C1+C2) = (1/20)*(C1+C2).......(iii)
Therefore, C1+C2 = 20K ......(iv)

Now, I can also solve (i) and (ii):
1.1C1 + 0.9C2 = 1.05C1 + 1.05C2 => C1 = 3C2 .......(v)

Using (iv) and (v), C1=5K and C2 = 15K

S1 =5K(1.1) = 5.5K
S2 = 13.5K.

Something is wrong. Can someone please help me?

NB: I know another easy method to solve this by using backtrace. However, I am not sure what's wrong with above equations...Please help me

Well i recommend a little easier approach.

Lets go by Options...

Since First car is to make money and second to loose. Right!

A & B cannot be answers as their prices are too low to make 10% as 1000.

C can also not be answer, as 10% of 11000 = 1100 and loss on second car 10% of 9000 = -900 will not make 1000 overall gain.

Answer should be D.

10% of 15000 - 10% of 5000 = 1000, which is also 5% of (15000+5000).

Option E also gives $ 1000/- profit, but not 5% overall profit, hence rejected.

voodoo_child wrote:

Shalabh's Quants wrote:

voodoo_child wrote:A car dealership sold two cars: the first car at a 10% profit and the second car at a 10% loss, which gave them an overall profit margin of 5% from these two sales. If the dealership's total profit was $1000, what was the sale price of each car?

$5,000 and $1,000
$9,000 and $5,000
$11,000 and $9,000
$15,000 and $5,000
$20,000 and $10,000

OA - D

S1 = selling price of car1
S2 = selling price of car2

S1 = 1.1C1; S2=0.9C2 ......(i)

S1 + S2 = 1.05(C1+C2) ...(ii)

Profit = $1000 = (S1+S2) - (C1+C2) = (1/20)*(C1+C2).......(iii)
Therefore, C1+C2 = 20K ......(iv)

Now, I can also solve (i) and (ii):
1.1C1 + 0.9C2 = 1.05C1 + 1.05C2 => C1 = 3C2 .......(v)

Using (iv) and (v), C1=5K and C2 = 15K

S1 =5K(1.1) = 5.5K
S2 = 13.5K.

Something is wrong. Can someone please help me?

NB: I know another easy method to solve this by using backtrace. However, I am not sure what's wrong with above equations...Please help me

Well i recommend a little easier approach.

Lets go by Options...

Since First car is to make money and second to loose. Right!

A & B cannot be answers as their prices are too low to make 10% as 1000.

C can also not be answer, as 10% of 11000 = 1100 and loss on second car 10% of 9000 = -900 will not make 1000 overall gain.

Answer should be D.

10% of 15000 - 10% of 5000 = 1000, which is also 5% of (15000+5000).

Option E also gives $ 1000/- profit, but not 5% overall profit, hence rejected.

Thanks but what's wrong with my method? Do you mind highlighting it?

Thanks