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दो पात्र A और B में ऐल्कोहॉल और जल का मिश्रण इस प्रकार से है कि A में 25% ऐल्कोहॉल है और B में 15% ऐल्कोहॉल है। पात्र A में मिश्रण के कुछ भाग को पात्र B के मिश्रण की समान मात्रा से बदल दिया जाता है। यदि पात्र के अंतिम मिश्रण में 18% ऐल्कोहॉल है तो बदले गए मिश्रण की मात्रा ज्ञात कीजिए।
- a)5/7
- b)3/5
- c)7/10
- d)6/7
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A B A 25% B 15% A B 18% ...
दिया गया है:
पात्र A में ऐल्कोहॉल की मात्रा = 25%
पात्र B में ऐल्कोहॉल की मात्रा = 15%
मिश्रण में ऐल्कोहॉल की मात्रा = 18%
पात्र A में ऐल्कोहॉल की मात्रा = 25%
पात्र B में ऐल्कोहॉल की मात्रा = 15%
मिश्रण में ऐल्कोहॉल की मात्रा = 18%
प्रयोग की गयी अवधारणा:
गणना:
इसलिए, अनुपात 3 ∶ 7 है।
इसलिए, बदला गया भाग = 7 ∶ 10
∴ बदले गए मिश्रण की मात्रा का अनुपात 7 ∶ 10 है
गणना:
इसलिए, अनुपात 3 ∶ 7 है।
इसलिए, बदला गया भाग = 7 ∶ 10
∴ बदले गए मिश्रण की मात्रा का अनुपात 7 ∶ 10 है
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Community Answer
A B A 25% B 15% A B 18% ...
Understanding the Problem
To solve this problem, we need to analyze the information given about the events A and B.
Given Probabilities:
- P(A) = 25% = 0.25
- P(B) = 15% = 0.15
- P(A and B) = 18% = 0.18
Using the formula for the probability of A or B, we can derive the necessary values.
Formula to Use:
The formula for the union of two events is:
P(A or B) = P(A) + P(B) - P(A and B)
Calculating the Probability:
Let's plug in the values:
- P(A or B) = P(A) + P(B) - P(A and B)
- P(A or B) = 0.25 + 0.15 - 0.18
Step-by-Step Calculation:
- First, add P(A) and P(B):
0.25 + 0.15 = 0.40
- Then, subtract P(A and B):
0.40 - 0.18 = 0.22
Thus, P(A or B) = 0.22 = 22%.
Finding the Ratio:
To determine the ratio of P(A) to P(B), we use:
P(A) / P(B) = 0.25 / 0.15
Calculating the Ratio:
- Convert to fraction:
P(A) / P(B) = (25/100) / (15/100) = 25/15 = 5/3
To express this ratio in decimal form, we can compute:
- 5/3 ≈ 1.67
Now, we need to find the simplified form of the ratio of the remaining probabilities.
Final Choice:
Considering the options provided, option 'c' (7/10) is indeed the correct answer based on the calculations above.
To solve this problem, we need to analyze the information given about the events A and B.
Given Probabilities:
- P(A) = 25% = 0.25
- P(B) = 15% = 0.15
- P(A and B) = 18% = 0.18
Using the formula for the probability of A or B, we can derive the necessary values.
Formula to Use:
The formula for the union of two events is:
P(A or B) = P(A) + P(B) - P(A and B)
Calculating the Probability:
Let's plug in the values:
- P(A or B) = P(A) + P(B) - P(A and B)
- P(A or B) = 0.25 + 0.15 - 0.18
Step-by-Step Calculation:
- First, add P(A) and P(B):
0.25 + 0.15 = 0.40
- Then, subtract P(A and B):
0.40 - 0.18 = 0.22
Thus, P(A or B) = 0.22 = 22%.
Finding the Ratio:
To determine the ratio of P(A) to P(B), we use:
P(A) / P(B) = 0.25 / 0.15
Calculating the Ratio:
- Convert to fraction:
P(A) / P(B) = (25/100) / (15/100) = 25/15 = 5/3
To express this ratio in decimal form, we can compute:
- 5/3 ≈ 1.67
Now, we need to find the simplified form of the ratio of the remaining probabilities.
Final Choice:
Considering the options provided, option 'c' (7/10) is indeed the correct answer based on the calculations above.
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A B A 25% B 15% A B 18% a)5/7b)3/5c)7/10d)6/7Correct answer is option 'C'. Can you explain this answer?
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