units sold after the reduction

sanju09 wrote:In order to increase its sales a production company reduces the price of its units by 20 percent, which results in an increase of 28 percent in its sales. What is the percent increase in the units sold after the reduction?
(A) 25
(B) 30
(C) 45
(D) 60
(E) 75


Made up

let the price of the unit be x, and sales be y, No. of units sold=y/x;
after reduction price of the unit=.8x and sales becomes 1.28y, No. of units sold=1.28y/.8x;

hence percent increase in the unit sold={(1.28y/.8x-y/x)/(y/x)}*100;
(128/80-1)*100; 48/80*100=60% hence D

Hi,

I think there's a mistake in the question, since the stem clearly states that there's a 28% increase in sales (a term which usually refers to the number of units sold). Did you mean to say that there's a 28% increase in gross revenue?

Alternatively, if that part of the question is correct, then the final sentence needs to be changed to "what is the percent increase in revenue after the reduction?".

As it stands, the common interpretation would be that there's a 28% increase in the number of units sold, which clearly isn't what you intended.

sanju09 wrote:In order to increase its sales a production company reduces the price of its units by 20 percent, which results in an increase of 28 percent in its sales. What is the percent increase in the units sold after the reduction?
(A) 25
(B) 30
(C) 45
(D) 60
(E) 75


Made up

Stuart Kovinsky wrote:Hi,

I think there's a mistake in the question, since the stem clearly states that there's a 28% increase in sales (a term which usually refers to the number of units sold). Did you mean to say that there's a 28% increase in gross revenue?

Alternatively, if that part of the question is correct, then the final sentence needs to be changed to "what is the percent increase in revenue after the reduction?".

As it stands, the common interpretation would be that there's a 28% increase in the number of units sold, which clearly isn't what you intended.

sanju09 wrote:In order to increase its revenue a production company reduces the price of its units by 20 percent, which results in an increase of 28 percent in its revenue. What is the percent increase in the units sold after the reduction?
(A) 25
(B) 30
(C) 45
(D) 60
(E) 75


Made up

Mistake admitted and edited, thanks

manpsingh87 wrote:

sanju09 wrote:In order to increase its revenue a production company reduces the price of its units by 20 percent, which results in an increase of 28 percent in its revenue. What is the percent increase in the number of units sold after the reduction?
(A) 25
(B) 30
(C) 45
(D) 60
(E) 75


Made up

let the price of the unit be x, and sales be y, No. of units sold=y/x;
after reduction price of the unit=.8x and sales becomes 1.28y, No. of units sold=1.28y/.8x;

hence percent increase in the unit sold={(1.28y/.8x-y/x)/(y/x)}*100;
(128/80-1)*100; 48/80*100=60% hence D

Always avoid using more than necessary variables to save time and calculation intricacies.

If initially 100 was the price of each unit and 100 happened to be the number of units sold, then 100 × 100 = 10,000 was the revenue.

Now, if the price of each unit becomes 80 and it results in an increase of x percent in the number of units sold after the reduction, then according to the question the revenue becomes 28 percent more than 10,000, mathematically

80 (100 + x) = 12,800

80 x = 4,800 or x = [spoiler]60%


D[/spoiler]