Directions : Each question below is followed by two statements A and B...
Let, the secretary spoke for x min. Then from statement A.
Number of words = 50 x
From statement B,
Number of words spoken = (x + 10) ( 50 –4)
50 x = 46 (x + 10)
x = 460/4 = 115 min
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Directions : Each question below is followed by two statements A and B...
Question Analysis:
The question asks about the duration of the secretary's speech. We need to determine if the information provided in both statements A and B is sufficient to answer the question.
Statement A: He spoke at an average of 50 words per minute.
Statement B: He would have spoken for 10 minutes extra had his speech rate been 4 words less per minute.
Initial Thoughts:
Statement A provides the average speech rate of the secretary, while statement B gives information about the potential increase in speech duration if the rate were slower. To determine the exact duration of the speech, we need both pieces of information.
Detailed Explanation:
To calculate the duration of the speech, we need to know the total number of words spoken. Statement A tells us that the secretary spoke at an average rate of 50 words per minute. However, without knowing the total number of words, we cannot determine the duration of the speech.
Statement B provides information about what would have happened if the speech rate were slower. It states that the secretary would have spoken for an additional 10 minutes if the speech rate were 4 words less per minute. This information alone does not give us the exact duration of the speech.
Combining the Statements:
By combining the information from both statements, we can determine the exact duration of the speech.
Let's assume the total number of words spoken is "W" and the duration of the speech is "D" minutes.
From statement A, we know that the average speech rate is 50 words per minute. Therefore, the total number of words spoken (W) can be calculated as W = 50D.
From statement B, we know that the secretary would have spoken for an additional 10 minutes if the speech rate were 4 words less per minute. This means that the original speech rate is 50 words per minute, and if it were reduced by 4 words per minute, the speech rate would be 46 words per minute. So, we can write the equation as W = 46(D + 10).
By equating both equations, we can solve for D, the duration of the speech.
50D = 46(D + 10)
50D = 46D + 460
4D = 460
D = 115
Hence, by combining both statements, we can determine that the secretary's speech lasted 115 minutes.
Conclusion:
The data provided in both statements A and B together are sufficient to answer the question about the duration of the secretary's speech. Therefore, the correct answer is option C.