10% fewer blue dresses were sold on Tuesday than on Monday, but 10% more red dresses were sold on Tuesday than Monday.

So the additional number of red dresses sold on Tuesday could cover the decrease in blue dresses sold on Tuesday, and still result in an overall increase of 5% of all dresses sold as compared to Monday.

This tells us that :

10% of red dresses sold on Monday = 10% of blue dresses sold on Monday + 5% of all dresses sold on Monday.

Multiply by 10 ,

100% of red dresses sold on Monday
= 100% of blue dresses sold on Monday
+ 50% of all dresses sold on Monday.

This is the same as saying :

Red dresses sold on Monday = blue dresses sold on Monday + ½ blue dresses + ½ red dresses sold on Monday

(50% of all dresses sold on Monday = 50% of blue dresses sold on Monday + 50% of red dresses sold on Monda


Let R represent total number of red dress sold on Monday and B represent total number of blue dresses sold on Monday.

From our earlier equation,

R = B + ½R + ½B
Multiply both sides of equation by 2,

2R = 2B + R + B
R = 3B

So ratio of red to blue sold on Monday is 3 : 1, since 1 unit of red equals 3 units of blue. Total is 4 units.


Percentage sold on Monday that were red
= 3/4 x 100%
= 75%

Alternatively, let number of red dresses sold on Monday be 10R, and number of blue dressses sold on Monday be 10B.
Total = 10A + 10B

On Tuesday,

Red dresses sold = 11R
Blue dresses sold = 9B
Total = 11R + 9B

Total sold on Tuesday is 5% more than Monday.

5% of Monday total = 5% of red on Monday + 5% of blue on Monday

5% of red on Monday is ½R
5% of blue on Monday is ½B


So 11R + 9B = 10R + 10B + ½R + ½B

11R + 9B = 10½R + 10½B
½R = 1½B
R = 3B

Ratio of red to blue is 3 : 1 , since 1 unit of red is equal to 3 times 1 unit of blue.


Total = 4 units

Percentage = 3/4 x 100% = 75%