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A bag contains 12 balls of two different colours, out of which x are white. One ball is drawn at random. If 6 more white balls are put in the bag, the probability of drawing a white ball now will be double to that of the previous probability of drawing a white ball. Then, the value of x is _____.
- a)3
- b)4
- c)5
- d)6
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A bag contains 12 balls of two different colours, out of which x are w...
Understanding the Problem
To solve the problem, we need to establish the initial conditions and the subsequent changes in the bag's contents.
Initial Setup
- Total balls in the bag = 12
- White balls = x
- Therefore, non-white balls = 12 - x
Initial Probability of Drawing a White Ball
The probability (P1) of drawing a white ball initially is calculated as:
- P1 = Number of white balls / Total number of balls = x / 12
After Adding More White Balls
When 6 more white balls are added:
- New number of white balls = x + 6
- New total number of balls = 12 + 6 = 18
New Probability of Drawing a White Ball
The new probability (P2) of drawing a white ball becomes:
- P2 = (x + 6) / 18
Setting Up the Equation
According to the problem, the new probability is double the initial probability:
- P2 = 2 * P1
Substituting the probabilities:
- (x + 6) / 18 = 2 * (x / 12)
Solving the Equation
Cross-multiplying gives:
- 12(x + 6) = 36x
- 12x + 72 = 36x
- 72 = 36x - 12x
- 72 = 24x
- x = 72 / 24
- x = 3
Conclusion
Thus, the value of x, the number of white balls initially in the bag, is 3. The correct answer is option 'A'.
To solve the problem, we need to establish the initial conditions and the subsequent changes in the bag's contents.
Initial Setup
- Total balls in the bag = 12
- White balls = x
- Therefore, non-white balls = 12 - x
Initial Probability of Drawing a White Ball
The probability (P1) of drawing a white ball initially is calculated as:
- P1 = Number of white balls / Total number of balls = x / 12
After Adding More White Balls
When 6 more white balls are added:
- New number of white balls = x + 6
- New total number of balls = 12 + 6 = 18
New Probability of Drawing a White Ball
The new probability (P2) of drawing a white ball becomes:
- P2 = (x + 6) / 18
Setting Up the Equation
According to the problem, the new probability is double the initial probability:
- P2 = 2 * P1
Substituting the probabilities:
- (x + 6) / 18 = 2 * (x / 12)
Solving the Equation
Cross-multiplying gives:
- 12(x + 6) = 36x
- 12x + 72 = 36x
- 72 = 36x - 12x
- 72 = 24x
- x = 72 / 24
- x = 3
Conclusion
Thus, the value of x, the number of white balls initially in the bag, is 3. The correct answer is option 'A'.
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Community Answer
A bag contains 12 balls of two different colours, out of which x are w...
It is given that, total number of balls = 12
Number of white balls = x
∴ Probability of getting a white ball = x/12
Now, 6 white balls are added.
Total number of balls = 12 + 6 = 18
Number of white balls = x + 6
Probability of getting a white ball
= x + 6 / 18
According to the question,
x + 6 / 18 = 2 x x/12
⇒ x + 6 - 3x ⇒ x - 3
Number of white balls = 3
Number of white balls = x
∴ Probability of getting a white ball = x/12
Now, 6 white balls are added.
Total number of balls = 12 + 6 = 18
Number of white balls = x + 6
Probability of getting a white ball
= x + 6 / 18
According to the question,
x + 6 / 18 = 2 x x/12
⇒ x + 6 - 3x ⇒ x - 3
Number of white balls = 3
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A bag contains 12 balls of two different colours, out of which x are white. One ball is drawn at random. If 6 more white balls are put in the bag, the probability of drawing a white ball now will be double to that of the previous probability of drawing a white ball. Then, the value of x is _____.a)3b)4c)5d)6Correct answer is option 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A bag contains 12 balls of two different colours, out of which x are white. One ball is drawn at random. If 6 more white balls are put in the bag, the probability of drawing a white ball now will be double to that of the previous probability of drawing a white ball. Then, the value of x is _____.a)3b)4c)5d)6Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contains 12 balls of two different colours, out of which x are white. One ball is drawn at random. If 6 more white balls are put in the bag, the probability of drawing a white ball now will be double to that of the previous probability of drawing a white ball. Then, the value of x is _____.a)3b)4c)5d)6Correct answer is option 'A'. Can you explain this answer?.
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ample number of questions to practice A bag contains 12 balls of two different colours, out of which x are white. One ball is drawn at random. If 6 more white balls are put in the bag, the probability of drawing a white ball now will be double to that of the previous probability of drawing a white ball. Then, the value of x is _____.a)3b)4c)5d)6Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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