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09 Oct 2010, 01:26
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
78% (02:18) correct
22%
(02:52)
wrong
based on 656
sessions
History
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Working together, John and Jack can type 20 pages in one hour. If they would be able to type 22 pages in one hour if Jack increases his typing speed by 25%, what is the ratio of Jack's normal typing speed to that of John?
A. 1/3
B. 2/5
C. 1/2
D. 2/3
E. 3/5
A. 1/3
B. 2/5
C. 1/2
D. 2/3
E. 3/5
09 Oct 2010, 01:51
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Barkatis
Let the rate of John be \(x\) pages per hour and the rate of Jack \(y\) pages per hour. Then as we can sum the rates and \(rate*time=job\): \((x+y)*1=20\) --> \(x+y=20\);
"They would be able to type 22 pages in one hour if Jack increases his typing speed by 25%": \((x+1.25y)*1=22\) --> \(x+1.25y=22\);
Question: \(\frac{y}{x}=?\)
Subtract (1) from (2) --> \(x+1.25y-(x+y)=22-20\) --> \(0.25y=2\) --> \(y=8\) --> \(x=12\) --> \(\frac{y}{x}=\frac{8}{12}=\frac{2}{3}\).
Answer: D.
OR: as by increasing the rate of Jack by 25% 2 more pages can be typed in one hour than we can directly write: \(0.25y=2\) --> --> \(y=8\) --> \(x=12\) --> \(\frac{y}{x}=\frac{8}{12}=\frac{2}{3}\).
Answer: D.
09 Oct 2010, 01:50
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Barkatis
Lets say John types x pages an hour and Jack types y pages an hour.
We know that x+y=20
Jack increase speed by 25% means he will type 1.25y pages an hour.
So we get x+1.25y=22
We need to know the ratio of Jack's speed to John's speed. This is going to be proportional to the number of pages each can type in an hour, hence (y/x).
Subtracting both : 0.25y=2 so y=8 ... so x=12
(y/x)=2/3
Answer is (D)
