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E
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Difficulty:
55%
(hard)
Question Stats:
67% (02:46) correct
33%
(03:03)
wrong
based on 132
sessions
History
Date
Time
Result
Not Attempted Yet
Of the 24 students in a typing class, 9 can type a basic business letter in an average of \(5 \ \ \frac{1}{2}\) minutes, while the other 15 students can type the same letter in an average of \(7 \ \ \frac{1}{5}\) minutes. What is the average amount of time it takes, in minutes, for a student in the typing class to type a basic business letter?
A 6 1/8
B 6 11/80
C 6 7/20
D 6 1/2
E 6 9/16
A 6 1/8
B 6 11/80
C 6 7/20
D 6 1/2
E 6 9/16
30 Jul 2021, 22:22
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Solution:
Bunuel The question has a couple of typo errors. Instead of \(512\), it should be \(5\frac{1}{2}\) and instead of \(715\), it should be \(7\frac{1}{5}\)
Now coming to the solution.
We know 9 students can type a basic business letter in an average of \(5\frac{1}{2}\) minutes.
So, total time these 9 students take \(=9\times 5\frac{1}{2}=\frac{9\times 11}{2}=\frac{99}{2}\)
We know 15 students can type a basic business letter in an average of \(7\frac{1}{5}\) minutes.
So, total time these 15 students take \(=15\times 7\frac{1}{5}=\frac{15\times 36}{5}=108\)
Total time taken by these 24 students \(= \frac{99}{2} + 108=\frac{(99+216)}{2}=\frac{315}{2}\)
Thus the average amount of time taken by any student \(= \frac{315}{2\times 24}=\frac{315}{48}=6\frac{9}{16}\)
Hence the right answer is Option E.
Bunuel The question has a couple of typo errors. Instead of \(512\), it should be \(5\frac{1}{2}\) and instead of \(715\), it should be \(7\frac{1}{5}\)
Now coming to the solution.
We know 9 students can type a basic business letter in an average of \(5\frac{1}{2}\) minutes.
So, total time these 9 students take \(=9\times 5\frac{1}{2}=\frac{9\times 11}{2}=\frac{99}{2}\)
We know 15 students can type a basic business letter in an average of \(7\frac{1}{5}\) minutes.
So, total time these 15 students take \(=15\times 7\frac{1}{5}=\frac{15\times 36}{5}=108\)
Total time taken by these 24 students \(= \frac{99}{2} + 108=\frac{(99+216)}{2}=\frac{315}{2}\)
Thus the average amount of time taken by any student \(= \frac{315}{2\times 24}=\frac{315}{48}=6\frac{9}{16}\)
Hence the right answer is Option E.
