Mary had two boxes filled with balls. The first box had red and white

Question

Mary had two boxes filled with balls. The first box had red and white balls in the ratio 1:4; the second box had red and white balls in the ratio 3:2. When the balls in the two boxes were mixed into an empty bigger box, the new box had 40% red balls. If the bigger box had 600 balls in all, how many white balls did the second box have?

A. 120
B. 180
C. 200
D. 240
E. 300

A. 120
B. 180
C. 200
D. 240
E. 300

yogi.0195 · Answer

Total number of balls in first box can be assumed to be x

Total number of balls in second box be y.

We can then develop two equations using the information given in the question.

mattisweb · Answer

Box 1: R/W = 1/4
Box 2: R/W = 3/2
Bigger Box: R/W = 4/6 
(It is 4/6 to get 4/(4+6) = 40% Red balls.) 
Total white balls in bigger box 10x = 600 -> x = 60 -> 4x/6x (pick 6x, as white is in denumerator). 
6 * 60 = 360 white balls -> 240 Red Balls.

Set up equations for white and red balls, respectively, using the ratios provided. 
1) 1x + 3y = 240 -> x = 240 - 3y
2) 4x + 2y = 360
Subtract 2 times the first equation from 3 times the second equation to get 10x = 600

Solve -> x,y = (60,60) 
White balls in second box: 2*60 = 120

ANS: A

ravi1522 · Answer

Box 1: R/W = 1/4 (20% red ball )
Box 2: R/W = 3/2 (60% red ball )
Bigger Box: 40 % of red ball 
so to get 40% it is just average of both so it means both have to mixed in equal proportion 
each box will be of 300 balls each 
Box 2 will have 120 balls

Hence option A is correct

Dereno · Answer

FIRST BOX, the number of Red balls : White balls = 1 : 4

SECOND BOX, the number of Red balls : White balls = 3 : 2

when the two balls are mixed, we get a total of 600 balls. The number of Red Balls = 40% * 600 = 240

The number of Blue Balls = 60% * 600 = 360

Using Alligations and Mixtures, ( RED Balls )

First box ————————— Total ————————- Second box

1/5 ———————————— (2/5) ——-——————— (3/5)

Multiplying by 5 throughout, we get

1 ————————————- 2 ————————————- 3

ratio of  First box : Second Box = 1:1

With a total of 600 Balls, the balls in the first Box and Second Box are 300 balls each respectively.

The number of WHITE BALLS in the Second box = ?

Red : White = 3:2 = 5x

so, 5x = 300

x = 60

The number of White Balls = 2x = 2*60 =  120 Balls .

Option A

ExpertsGlobal5 · Answer

Good job. Excellent use of alligation...!

Bunuel · Answer

Experts' Global Video Explanation:

https://www.youtube.com/watch?v=mey1Tk5dl84

SmileAndSolve · Answer

I thought the question meant  bigger  of the 2 boxes because the combined one would be the  biggest  box.

(It did feel fishy when I was getting 600 as total value for both boxes but had spent 2 mins so marked D accordingly :/)

undeniablevirgin · Answer

Let the ratio of red:white in Box 1 be 1x : 4x, so Box 1 has a total of 5x balls.
 Let the ratio of red:white in Box 2 be 3y : 2y, so Box 2 has a total of 5y balls.

Step 1 - Total balls equation: 
 Since the combined box has 600 balls:
 5x + 5y = 600 → x + y = 120 ... (1)

Step 2 - Total red balls equation: 
 40% of 600 = 240 red balls in total. Red balls come from x (Box 1) and 3y (Box 2):
 x + 3y = 240 ... (2)

Step 3 - Solve: 
 Subtracting (1) from (2): 2y = 120 so y = 60

Step 4 - Answer: 
 White balls in Box 2 = 2y = 2(60) =  120
 
 Answer: A. 120

Mary had two boxes filled with balls. The first box had red and white

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Mary had two boxes filled with balls. The first box had red and white

Prep Toolkit

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