On January 1st, the selling price of a car was $A. The price initially

Question

On January 1st, the selling price of a car was $A. The price initially increased by X% on February 1st, and then decreased by X% on March 1st, which resulted in an overall decrease in the price of the car by $1,400. What would have been the overall decrease in price had the increase on February 1st and decrease on March 1st been by 2X%??

A) $1,400
B) $2,800
C) $4,200
D) $5,600
E) $11,200

A) $1,400
B) $2,800
C) $4,200
D) $5,600
E) $11,200

VivekSri · Answer

OA is D

Todercap · Answer

Original scenario: 
Jan:  $A 
Feb: increased by X% -  A(1+X\100) 
Mar: decreased by X% - (A+AX\100)(1-X\100) = A+AX\100-AX\100-AX^2\100 =  A-AX^2\100

Overall decrease = 1400

A-(A-AX^2\100)=1400 =  AX^2\100=1400

New scenario 
Jan:  $A 
Feb: increased by 2X% -  A(1+2X\100) 
Mar: decreased by X% - (A+2AX\100)(1-2X\100) = A+2AX\100-2AX\100-4AX^2\100 =  A-4AX^2\100

Overall decrease in new scenario:
A-(A-4AX^2\100) = 4AX^2\100

NOTE: That's 4 time the decrease of the original scenario.
1400*4 = 4000+1600=5600

Answer choice D.

sherlocked221B · Answer

Please find the solution in the attached image.
 Answer = 5600

Advait01 · Answer

A more simple method would be to consider values of A and X as 100/- and 10% respectively.
Jan 1 - 100/-
Feb 1 - 110/-
Mar 1 - 99/-
Diff 1= 1/-

Now X = 20%;
Jan 1 - 100/-
Feb 1 - 120/-
Mar 1 - 96/-
Diff 2 = 4/-
So, 4 times from previous
Now from question statement, 
Diff 1 = 1440
Therefore, Diff 2 has to be Approx 5600

KarishmaB · Answer

Two successive equal percentage changes of x% each, one an increase and the other a decrease lead to a decrease of  \frac{x^2}{100}  %.

So we are given that  \frac{x^2}{100} % of A is $1400.

If instead, the increase and decrease is of 2x%, then the overall change will be a decrease of  \frac{(2x)^2}{100}  % i.e.  \frac{4x^2}{100}%  of A.

Since  \frac{x^2}{100} % of A is 1400,  \frac{4x^2}{100} % of A will be 4*1400 =5,600

Answer (D)

On January 1st, the selling price of a car was $A. The price initially

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On January 1st, the selling price of a car was $A. The price initially

Prep Toolkit

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