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Work/Rate

by satishchandra » Tue Dec 27, 2011 1:58 am
Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

(A) 41.4
(B) 34.1
(C) 13.4
(D) 12.4
(E) 10.8

I know this is a simple problem. It took appx 3 mins for me to solve, and I thought my appoach was lengthy.
I could eliminate (c), (D), (E) in just 20 seconds but painfully had to go for complete solution to pick right option between A and B.
I will appreciate if anyone could post quicker approach.
For those who excite about knowing OA, IT's A
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by Anurag@Gurome » Tue Dec 27, 2011 2:17 am
satishchandra wrote:Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

(A) 41.4
(B) 34.1
(C) 13.4
(D) 12.4
(E) 10.8

I know this is a simple problem. It took appx 3 mins for me to solve, and I thought my appoach was lengthy.
I could eliminate (c), (D), (E) in just 20 seconds but painfully had to go for complete solution to pick right option between A and B.
I will appreciate if anyone could post quicker approach.
For those who excite about knowing OA, IT's A
Let Jim types the report in x hours and let Mary type the report in y hours.
1/x + 1/y = 1/12.5
1/x + 1/30 = 1/12.5
(30 + x)/30x = 1/12.5
375 + 12.5x = 30x
375 = 17.5x
x = 150/7

Let Jim edits the report in a hours and let Mary edit the report in b hours.
1/a + 1/b = 1/7.5
1/12 + 1/b = 1/7.5
b + 12 = 12b/7.5
7.5b + 90 = 12b
90 = 4.5b
b = 20

Therefore, time taken by Jim to type the report and for Mary to edit it = 150/7 + 20 = 41.4

The correct answer is A.
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by pemdas » Tue Dec 27, 2011 2:45 am
1/30 + 1/J=1/12.5
1/M + 1/12=1/7.5 solve for M (speed EDITS) and J (speed TYPES)

(when one types the other is unknown, the same with edition done)

1/J=2/25-1/30=14/300=7/150 (150/7 Jim needs to type) <- tip: reciprocal for time/work conversion
1/M=2/15-1/12=3/60=1/20 (20 hours Mary need to edit) <- tip: reciprocal for time/work conversion

combined time (20+21.4)=41.4 hours

ans.A
satishchandra wrote:Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

(A) 41.4
(B) 34.1
(C) 13.4
(D) 12.4
(E) 10.8

I know this is a simple problem. It took appx 3 mins for me to solve, and I thought my appoach was lengthy.
I could eliminate (c), (D), (E) in just 20 seconds but painfully had to go for complete solution to pick right option between A and B.
I will appreciate if anyone could post quicker approach.
For those who excite about knowing OA, IT's A
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by ronnie1985 » Tue Dec 27, 2011 3:38 am
The question can be solved effectively by table:-

Type Edit Time Taken by The Question
Mary 0.03 0.05 20
Jim 0.05 0.083333333 21.42857143
Total 0.08 0.133333333
Total Time = 41.42857143
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by happymanocha » Tue Dec 27, 2011 8:19 am
Here is how i will solve the problem:
From first statement: 1/30+1/JT=2/25
From 2nd statement: 1/12+1/ME=2/15
Sum of first and 2nd statement = 1/30+1/12+1/JT+1/ME=2/25+2/15

1/JT+1/ME=87/900

What we need to calculate is reciprocal of it i.e 900/87.

Ans: [color=white]A[/color]
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