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Dave and Diana at work

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by sanju09 » Tue Feb 24, 2009 4:07 am
If Dave works alone he will take 20 more hours to complete a task than if he worked with Diana to complete the task. If Diana works alone, she will take 5 more hours to complete the complete the task, then if she worked with Dave to complete the task? What is the ratio of the time taken by Dave to that taken by Diana if each of them worked alone to complete the task?

A. 4 : 1

B. 2 : 1

C. 10 : 1

D. 3 : 1

E. 1 : 2
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by bluementor » Tue Feb 24, 2009 4:31 am
Time taken if both worked together = T
Ratio of Dave : Diana = (20 + T) : (5 + T)

We can setup the following work equation:

1/(T+5) + 1/(T+20) = 1/T
(25 + 2T)/((20+T)(5+T)) = 1/T
25T + 2T^2 = 100 + 25T + T^2
T^2 = 100
T = 10

Therefore ratio = (20 + 10) : (5 + 10) = 30:15 = 2:1

Choose B.

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by sureshbala » Tue Feb 24, 2009 4:34 am
Let the time taken when Dave and Diana work together be x hrs.
Given that time taken by Dave alone = x+20hrs
and time taken by Diana alone = x+5 hrs.

Instead of going for a traditional way you can answer it quickly with a simple logic.

Dave and Diana together = xhrs
Dave alone= x+20.

Now from these two statements we can conclude that, work done by Dave in 20 hrs is done by Diana in x hrs. So Dave:Diana=20:x

Similarly,
Dave and Diana together = xhrs
Diana alone = x+5,
We can conclude that work done by Diana in 5 hrs is done by Dave in x hrs. So Dave: Diana = x:5

So we have 20/x = x/5
i.e x =10.

Hence the time ratio of Dave and Diana = 20:x = 2:1
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