Box A contains white, blue and red balls where the ratio of the number

Question

Box A contains white, blue and red balls where the ratio of the number of white balls to the number of blue balls is 1:2 and the ratio of the number of blue balls to the number of red balls is 4:3. Box B contains white balls and blue balls in the ratio 4:5. Box C contains only blue balls so that the ratio of the number of blue balls in Box C to the number of white balls in Box A is 3:2. If the total number of blue balls in all the three boxes is 45, what is the number of white balls in Box B?

(A) 4
(B) 8
(C) 12
(D) 14
(E) 16

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(A) 4
(B) 8
(C) 12
(D) 14
(E) 16

Posted from my mobile device

yashshukla1995 · Accepted Answer

Box A => ratio of White : Blue : Red = 2:4:3
 Therefore white marbles = 2k; Blue = 4k and Red = 3k

Box B =>. Ratio of White : Blue = 4:5
 Therefore White Marbles = 4k' and Blue Marbles = 5k'

Box C => Number of Blue Marbles = P

Given Ratio
 P/White Marbles in BoxA = 3/2 =>   = 3/2 => P=3k

Total Number of Blue Marbles = 45
 4k + 5k'+ P = 45 => 4k + 5k' + 3k = 45 => 7k + 5k' = 45

For k=5 and k'=2 the equation stands valid (Finding solution from One equation)

Hence No of white marbles = 4k' = 4*2 = 8;

Option B

Kinshook · Answer

Given: Box A contains white, blue and red balls where the ratio of the number of white balls to the number of blue balls is 1:2 and the ratio of the number of blue balls to the number of red balls is 4:3. Box B contains white balls and blue balls in the ratio 4:5. Box C contains only blue balls so that the ratio of the number of blue balls in Box C to the number of white balls in Box A is 3:2.

Asked: If the total number of blue balls in all the three boxes is 45, what is the number of white balls in Box B?

Box A contains white, blue and red balls where the ratio of the number of white balls to the number of blue balls is 1:2 and the ratio of the number of blue balls to the number of red balls is 4:3. 
Ratio of number of white, blue and red balls in Box A = 2:4:3
Let the number of white, blue and red balls in Box A be 2k, 4k & 3k respectively

Box B contains white balls and blue balls in the ratio 4:5. 
Let the number of white balls and blue balls in Box B be 4m & 5m respectively

Box C contains only blue balls so that the ratio of the number of blue balls in Box C to the number of white balls in Box A is 3:2.

Number of blue balls in Box C / 2k = 3/2 
Number of blue balls in Box C = 3k

The total number of blue balls in all the three boxes is 45 
4k + 5m + 3k = 45
7k + 5m = 45
k = (45-5m)/7
Since k & m are integers.
k = 5; m=2

The number of white balls in Box B = 4m = 4*2 = 8

IMO B

HarshaBujji · Answer

IMO B,

We can back track using options also. As the ratio is 4:5 , N.o white balls is 4 multiple.. Use this and check for each value.

In this case, Solving by putting the variables is the best approach. But it depends on the options

Ninni1628 · Answer

From the above sum, we can tell that the ratio amount/variable for Box A and Box C is the same. We can say that in Box A the ratio of W:B:R is : 2x:4x:3x in Box B, we can say that the ratio of W:B is 4y:5y in Box C, we can say that the ratio is in comparision to Box A, therefore, the ratio can be seen as W:B which is 2:3 Now, we know the actual number of Blue Balls which is 4x + 5x + 3x = 45 We can say that : 7x + 5y = 45 We know that the marbles exist in whole numbers only, therefore we can solve for two variables in this eqaution and we can say x= 5 y=2 From substituting the value of y with 4, we know that 4*2=8

Box A contains white, blue and red balls where the ratio of the number

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Box A contains white, blue and red balls where the ratio of the number

Prep Toolkit

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