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A trader marked the price of a car

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A trader marked the price of a car

by emdadul28 » Mon Feb 13, 2017 8:33 am
A trader marked the price of a car 20% above the cost price and allowed the purchaser 5% discount on the marked price there by gained Rs.8400. Find the cost price of the car?


A. Rs.60000
B. Rs.75000
C. Rs.68400
D. Rs.78400
E. Rs.88400

Ans: A

[PLEASE GIVE DETAIL SOLUTIONS. THANKS IN ADVANCE]
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by Brent@GMATPrepNow » Mon Feb 13, 2017 8:58 am
emdadul28 wrote:A trader marked the price of a car 20% above the cost price and allowed the purchaser 5% discount on the marked price there by gained Rs.8400. Find the cost price of the car?


A. Rs.60000
B. Rs.75000
C. Rs.68400
D. Rs.78400
E. Rs.88400

Ans: A

[PLEASE GIVE DETAIL SOLUTIONS. THANKS IN ADVANCE]
Who gained Rs.8400?
Did the purchaser save that much money or does Rs.8400 represent the trader's profit?


NOTE: When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

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by Brent@GMATPrepNow » Mon Feb 13, 2017 9:06 am
emdadul28 wrote:A trader marked the price of a car 20% above the cost price and allowed the purchaser 5% discount on the marked price there by gained Rs.8400. Find the cost price of the car?


A. Rs.60000
B. Rs.75000
C. Rs.68400
D. Rs.78400
E. Rs.88400
I'll assume that Rs.8400 represents the trader's PROFIT

So solve this, let's first determine the net result of increasing the cost price by 20% and then decreasing the result by 5%

To do this, let's assign a nice value to the COST price.
Let 100 = the COST price

So, after a 20% increase, the NEW price = 120

Now let's decrease this NEW price by 5%
5% of 120 = 6, so the FINAL price = 120 - 6 = 114

If the COST price = 100, and the FINAL price is 114, then the trader makes a 14% PROFIT.
In other words, the trader's PROFIT = 14% of the COST PRICE

We're told that the PROFIT = Rs.8400
So, we know that Rs.8400 = 14% of the COST PRICE
In other words, 8400 = 0.14(COST PRICE)
So, COST PRICE = 8400/0.14 = 60,000

Answer: A

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by [email protected] » Mon Feb 13, 2017 10:29 am
Hi emdadul28,

This question can be solved by TESTing THE ANSWERS.

Let's TEST Answer A: 60,000

IF... the 'cost price' = 60,000
then the 'marked price' = (60,000)(1.2) = 72,000
and the 5% discount price = (72,000) - (72,000)(.05) = 72,000 - 3,600 = 68,400
so the overall seller's profit would be... 68,400 - 60,000 = 8,400

This is an exact match for what we were told, so this MUST be the answer.

Final Answer: A

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by Jeff@TargetTestPrep » Wed Feb 15, 2017 3:08 pm
emdadul28 wrote:A trader marked the price of a car 20% above the cost price and allowed the purchaser 5% discount on the marked price there by gained Rs.8400. Find the cost price of the car?


A. Rs.60000
B. Rs.75000
C. Rs.68400
D. Rs.78400
E. Rs.88400
We can let the cost of the car = c.

Since the trader marked the car up 20% and then down 5%, the car was sold for:

1.2 x 0.95 x c = 1.14c

Since the profit was Rs. 8400, we can create the following equation:

8400 = 1.14c - c

8400 = 0.14c

60,000 = c

Answer: A

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by Matt@VeritasPrep » Wed Feb 15, 2017 5:55 pm
Cost = x

Marked = x + .2x = 1.2x

Discount = 1.2x - .05*1.2x = 1.14x

.14x = 8400

x = 60000
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by Matt@VeritasPrep » Wed Feb 15, 2017 5:56 pm
It occurs to me that might be easier to see if I color coded it! :)

Cost = x

Marked = x + .2x = 1.2x

Discount = 1.2x - .05*1.2x = 1.14x

The cost was x and the final sale price is 1.14x, so the dealer nets .14x.

.14x = 8400

x = 60000
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by Jay@ManhattanReview » Thu Feb 16, 2017 4:26 am
emdadul28 wrote:A trader marked the price of a car 20% above the cost price and allowed the purchaser 5% discount on the marked price there by gained Rs.8400. Find the cost price of the car?


A. Rs.60000
B. Rs.75000
C. Rs.68400
D. Rs.78400
E. Rs.88400

Ans: A

[PLEASE GIVE DETAIL SOLUTIONS. THANKS IN ADVANCE]
Say the cost price = $100, thus the marked price = 100 + 20 = $120.

Thus, the discounted price = 120 - 5% of 120 = 120 - 6 = 114.

The gain = 114 - 100 = 14

Now $14 gain corresponds to the actual gain $8400. Thus 8400/14 = 600 is a factor that must be multiplied to cost price (100) to get the actual price.

Or, the cost price = 100*600 = [spoiler]$60,000[/spoiler].

Do not do the following in the step shown in blue.

Thus, the discounted price = 120 - 5 = 115.

This would the CP as 100*(8400/15)= $56,000.

However, there is no option as $56,000. So one may be safe if he/she commits this mistake. :)

The discount of 5% is applicable on marked price ($120) and not on Cost price ($100).

The correct answer: A

Hope this helps!

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