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Emptying a Jar.

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by vivekvijayan » Mon Oct 06, 2014 4:18 am
Danny and Ian are munching on a jar full of candies. Had Danny eaten alone it would have taken him 5 minutes to finish the candies in the jar. Had Ian eaten alone it would have taken him 10 minutes to finish half the jar.

Since both of them are eating simultaneously, how long would it take them to empty the jar?

2.5 minutes
3 minutes
3 minutes and 20 seconds
6 minutes and 40 seconds
4 minutes


I thought that this was an easy question. I got option C as the answer. But OA is E... Can someone pls explain this
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by gmatcracker0123 » Mon Oct 06, 2014 6:26 am
I guess you missed out on the fact that Ian alone would have taken 10 mins to finish half the jar.

Say there were 10 candies in the Jar.

Danny takes 5 mins to finish 10 candies.
Hence, in 1 min Danny eats 10/5 = 2 candies.

Ian takes 10 mins to finish half the jar i.e 10/2 = 5 Candies.
Hence , in 1 min Ian eats 5/10 = 1/2 a candy.

Hence together, in 1 min, Danny and Ian eat 2 + (1/2) = 2.5 candies
Therefore the time taken by them to finish of the jar = 10/2.5 = 4 mins

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by GMATGuruNY » Mon Oct 06, 2014 6:51 am
vivekvijayan wrote:Danny and Ian are munching on a jar full of candies. Had Danny eaten alone it would have taken him 5 minutes to finish the candies in the jar. Had Ian eaten alone it would have taken him 10 minutes to finish half the jar.

Since both of them are eating simultaneously, how long would it take them to empty the jar?

2.5 minutes
3 minutes
3 minutes and 20 seconds
6 minutes and 40 seconds
4 minutes
Let the number of candies in the jar = 20.
Since Danny can empty the jar in 5 minutes, Danny's rate = w/t = 20/5 = 4 candies per minute.
Since Ian can empty half the jar -- 10 candies -- in 10 minutes, Ian's rate = w/t = 10/10 = 1 candy per minute.
Combined rate for Danny and Ian = 4+1 = 5 candies per minute.
Thus:
At a combined rate of 5 candies per minute, the time for Danny and Ian to empty the whole jar of 20 candies = w/r = 20/5 = 4 minutes.

The correct answer is E.
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by [email protected] » Mon Oct 06, 2014 11:20 am
Hi vivekvijayan,

If you have 2 entities working together on a task AND you are given their individual rates to complete THAT task, then you can use to Work Formula to calculate how long it would take the two, working together, to complete the task.

Work Formula = (A)(B)/(A+B)

Here, we information on....

Danny = takes 5 minutes to finish the jar
Ian = takes 10 minutes to finish HALF the jar = 20 minutes to finish the jar

Danny = 5 minutes
Ian = 20 minutes

Now, plug those two values in for A and B....

(5)(20)/(5+20) = 100/25 = 4 minutes for the two, working together, to finish the jar.

Final Answer: E

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