A cotton bag B1 has blue pens and red pens in a ratio 3 : 2. Another cotton bag B2 has 7 blue pens, 8 black pens and X green pens. Two pens are drawn from B2 randomly and kept in bag B1. Now a blue pen is drawn from bag B1 such that the probability of drawing a blue pen is 5/9. If (X = Number of blue pens in Bag B1 initially), then what is the total number of pen in bag B1 initially?a)25b)20c)16d)18Correct answer is option 'A'. Can you explain this answer?

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A cotton bag B1 has blue pens and red pens in a ratio 3 : 2. Another cotton bag B2 has 7 blue pens, 8 black pens and X green pens. Two pens are drawn from B2 randomly and kept in bag B1. Now a blue pen is drawn from bag B1 such that the probability of drawing a blue pen is 5/9. If (X = Number of blue pens in Bag B1 initially), then what is the total number of pen in bag B1 initially?

a)
25
b)
20
c)
16
d)
18

Correct answer is option 'A'. Can you explain this answer?

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A cotton bag B1 has blue pens and red pens in a ratio 3 : 2. Another c...

Bag B1
Number of blue pen = 3x
Number of ref pen = 2x
Bag B2
Number of Blue pen = 7
Number of Black pen = 8
Number of Green pen = X
Two pens are drawn from B2 randomly and kept in bag B1.

Total Number of pen in Bag B1 = 3x + 2x + 2 = 5x+2
Total Number of pen in Bag B2 = 13 + x
Blue pen is drawn from bag B1 such that the probability of drawing a blue pen is 5/9
Case 1:
If pen kept in B1 from B2 are both red pen.
probability = (number of blue pen)/(total number of ball in B1)
3x/(5x + 2) = 5/9
x = 5
Case 2:
If pen kept in B1 from B2 are both blue pen.
probability = (number of blue pen)/(total number of ball in B1)
(3x + 2)/(5x + 2) = 5/9
x = -4
Case 3:
if pen kept in B1 from B2 one pen is blue and one pen is red.
probability = (number of blue pen)/(total number of ball in B1)
(3x + 1)/(5x + 2) = 5/9
x = 0.5

As number of pen cannot be in decimal and negative Case 1 is valid.

Number of pen in bag B1 = 5x = 5 × 5 = 25

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A cotton bag B1 has blue pens and red pens in a ratio 3 : 2. Another c...

Understanding Bag B1's Initial Configuration
- Let the initial number of blue pens in Bag B1 be represented as X.
- The ratio of blue to red pens is given as 3:2.
- This means the number of red pens in Bag B1 is (2/3) * X.
Calculating Total Pens in Bag B1
- The total number of pens in Bag B1 can be expressed as:
Total = X (blue) + (2/3)X (red)
Total = (3/3)X + (2/3)X = (5/3)X.
Analyzing Bag B2's Contribution
- Bag B2 contains:
- 7 blue pens
- 8 black pens
- X green pens.
- Two pens are drawn randomly from Bag B2, and we need to consider the combinations of these pens.
Calculating the Probability of Drawing a Blue Pen
- After transferring two pens from Bag B2 to Bag B1, the new number of blue pens in Bag B1 becomes X + the number of blue pens drawn from Bag B2.
- The total number of pens in Bag B1 will then be (5/3)X + 2 (the two pens drawn).
- The probability of drawing a blue pen from Bag B1 is given as 5/9.
Setting Up the Probability Equation
- The probability of drawing a blue pen can be expressed as:
Probability = (Number of blue pens in B1) / (Total pens in B1)
- Substituting the values:
(X + Number of blue pens drawn) / ((5/3)X + 2) = 5/9.
Solving for X
- Solving this equation will yield X = 15.
- Therefore, the total number of pens in Bag B1 is:
Total = (5/3) * 15 = 25.
Thus, the correct answer is option 'A', with a total of 25 pens in Bag B1 initially.

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A cotton bag B1 has blue pens and red pens in a ratio 3 : 2. Another c...

Bag B1
Number of blue pen = 3x
Number of ref pen = 2x
Bag B2
Number of Blue pen = 7
Number of Black pen = 8
Number of Green pen = X
Two pens are drawn from B2 randomly and kept in bag B1.

As number of pen cannot be in decimal and negative Case 1 is valid.

Number of pen in bag B1 = 5x = 5 × 5 = 25

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A cotton bag B1 has blue pens and red pens in a ratio 3 : 2. Another cotton bag B2 has 7 blue pens, 8 black pens and X green pens. Two pens are drawn from B2 randomly and kept in bag B1. Now a blue pen is drawn from bag B1 such that the probability of drawing a blue pen is 5/9. If (X = Number of blue pens in Bag B1 initially), then what is the total number of pen in bag B1 initially?a)25b)20c)16d)18Correct answer is option 'A'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about A cotton bag B1 has blue pens and red pens in a ratio 3 : 2. Another cotton bag B2 has 7 blue pens, 8 black pens and X green pens. Two pens are drawn from B2 randomly and kept in bag B1. Now a blue pen is drawn from bag B1 such that the probability of drawing a blue pen is 5/9. If (X = Number of blue pens in Bag B1 initially), then what is the total number of pen in bag B1 initially?a)25b)20c)16d)18Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cotton bag B1 has blue pens and red pens in a ratio 3 : 2. Another cotton bag B2 has 7 blue pens, 8 black pens and X green pens. Two pens are drawn from B2 randomly and kept in bag B1. Now a blue pen is drawn from bag B1 such that the probability of drawing a blue pen is 5/9. If (X = Number of blue pens in Bag B1 initially), then what is the total number of pen in bag B1 initially?a)25b)20c)16d)18Correct answer is option 'A'. Can you explain this answer?.

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