The ratio of red boxes to blue boxes in a certain warehouse is 12 to 1

Sorry, the initial ratio is 12/25 not 12/15. Edited.

Red / blue = 12/25
Red box = 12x
Blue box = 25x

24x/(25x+150) = 12/50 (ratio is halved when red is doubled and blue is increased by 150)
24x*50 = 300x + 1800
900x = 1800
x = 2

Red = 12 *2 = 24
Blue = 25 *2 = 50
Total = 74

Answer B
Ambarish

Hi All,

While many Test Takers would use an Algebraic approach to this question, it can also be solved by TESTing THE ANSWERS.

The initial ratio of red boxes to blue boxes is 12:25, which means that the initial number of red boxes is a MULTIPLE of 12 and the initial number of blue boxes is an equivalent MULTIPLE of 25. We're told to DOUBLE the number of red boxes and INCREASE the number of blue boxes by 150; the end result of these changes will HALVE the initial ratio (meaning it will become 12:50 or 6/25).

We're asked how many TOTAL boxes are currently in the warehouse.

Since we're DOUBLING the number of red boxes, we'll need to increase the number of blue boxes by a significant percent (to end up with a ratio that is 12:50). Since the increase of 150 blue boxes is 'fixed', the smaller the initial number of blue boxes, the greater the impact that the +150 will have on the ratio. Thus, we should start with the smaller answers.

Answer A: 37
IF....
Total boxes = 37
Red boxes = 12
Blue boxes = 25
After the increases:
Red boxes = 12(2) = 24
Blue boxes = 25+150 = 175
Final ratio = 24:175
This is NOT A MATCH for 12:50
Eliminate Answer A

Answer B: 74
IF....
Total boxes = 74
Red boxes = 24
Blue boxes = 50
After the increases:
Red boxes = 24(2) = 48
Blue boxes = 50+150 = 200
Final ratio = 48:200 = 24:100 = 12:50
This IS MATCH for 12:50, so this MUST be the answer.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Ratio = R/B = 12/25 or R = 12/25 B -----------(1)

2R/B+150 = 12/25*1/2 = 6/25 or we can say that 25R=3B+450 -------------(2)

solving (1) and (2) we get

B=50 and R = 24

so total boxes is B + R = 50+24=74

Hence B. 74 is the correct answer

OFFICIAL SOLUTION:

The ratio of red boxes to blue boxes in a certain warehouse is 12 to 25 - Red:Blue = 12x:25x.

If the number of the red boxes were doubled and the number of blue boxes were increased by 150 the ratio would be halved - (2*12x)/(25x + 150) = 1/2*12/25, which gives x = 2.

Total boxes = Red + Blue = 12x + 25x = 37x = 74.

Answer: B.

We are given that the ratio of red to blue boxes is 12 to 25, or equivalently, the number of red boxes is 12x and the number of blue boxes is 25x, for some integer x. If the number of red boxes doubles, we have 24x red boxes, and if the number of blue boxes increases by 150, we have 25x + 150. Since the ratio is now halved, the new ratio is 6 to 25 or 6/25. We can create the following equation:

24x/(25x + 150) = 6/25

25(24x) = 6(25x + 150)

Dividing each side by 6:

25(4x) = 25x + 150

100x = 25x + 150

75x = 150

x = 2

Thus, there are 12(2) + 25(2) = 74 boxes in the warehouse.

Answer: B

Original Ratio:

R : B = 12g : 25g

Total Boxes = 37g



If we were to DOUBLE (2*) the Red Boxes -----> 12g * (2) = 24g

and ADD + 150 to the Blue Boxes ------> (25g + 150)


The Ratio of R:B would be HALVED ------> R/B = (12/25) * (1/2) = 12/50 = 6/25


NEW RATIO of R : B ----

R/B = (24g) / (25g + 150) = 6/25

----Cancel 6 in the NUM----

(4g) / (25g + 150) = 1/25

----cross-multiply and Solve for the Unknown Ratio Multiplier = g ----

100g = 25g + 150

75g = 150

g = 2******


Total Number = 12g + 25g = 37g ------- where we just found that g = 2***

37g = 37*(2) = 74

-B-