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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
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Box A contains white, blue and red balls where the ratio of the number...
Understanding the Ratios in Box A
- Let the number of white balls in Box A be \( W \).
- The ratio of white to blue balls is \( 1:2 \), so the number of blue balls \( B \) is \( 2W \).
- The ratio of blue to red balls is \( 4:3 \), meaning that the number of red balls \( R \) is \( \frac{3}{4}B = \frac{3}{4}(2W) = \frac{3}{2}W \).
- Thus, in Box A:
- White balls, \( W \)
- Blue balls, \( 2W \)
- Red balls, \( \frac{3}{2}W \)
Analyzing Box B
- In Box B, the ratio of white to blue balls is \( 4:5 \).
- Let the number of white balls in Box B be \( 4x \) and blue balls be \( 5x \).
Understanding Box C
- Box C contains only blue balls.
- The ratio of blue balls in Box C to white balls in Box A is \( 3:2 \).
- Therefore, if the number of blue balls in Box C is \( C \), then \( C = \frac{3}{2}W \).
Total Blue Balls Calculation
- The total number of blue balls across all boxes is given as 45:
\[
B + 5x + C = 45
\]
- Substituting the values:
\[
2W + 5x + \frac{3}{2}W = 45
\]
- Combining the terms gives:
\[
\frac{7}{2}W + 5x = 45
\]
Solving for W and x
- To express \( W \) in terms of \( x \):
\[
7W + 10x = 90
\]
- Using integer values, we find \( W = 10 \) and \( x = 3 \).
Calculating White Balls in Box B
- The number of white balls in Box B is:
\[
4x = 4(3) = 12
\]
Thus, the number of white balls in Box B is 12 (Option B).
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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)4b)8c)12d)14e)16Correct answer is option 'B'. Can you explain this answer?
Question Description
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