If 600 men dig a 5.5 m wide, 4 m deep and 405 m long canal in half an

Question

If 600 men dig a 5.5 m wide, 4 m deep and 405 m long canal in half an hour, then how long a canal will 2500 men working for 6 hrs, dig if it is 10 m wide and 8 m deep?

A. 6452 m
B. 5568 3/4 m
C. 4082 m
D. 2694 1/3 m
E. 2604 m

sanjitscorps18 · Answer

Total volume dug by 600 men in 30 minutes = 5.5 x 4 x 405 cubic m
Total volume dug by 600 men in 1 hour = 2 x 5.5 x 4 x 405 cubic m
Total volume dug by 600 men in 6 hour = 6 x 2 x 5.5 x 4 x 405 cubic m
Total volume dug by 100 men in 6 hour = 2 x 5.5 x 4 x 405 cubic m
Total volume dug by 2500 men in 6 hour = 25 x 2 x 5.5 x 4 x 405 cubic m

Given that 2500 men dig in 6 hours = 10 x 8 x Length cubic m
=> 10 x 8 x Length = 25 x 2 x 5.5 x 4 x 405
=> Length = 25 x 5.5 x 405 / 10 = 5 x 55 x 405 / 20
=> Length = 5568.75 m

Option B

BrushMyQuant · Answer

If 600 men dig a 5.5 m wide, 4 m deep and 405 m long canal in half an hour

Let Rate of each men = R 
=> Rate of 600 men = 600*R = 600R
Work done = digging the canal = Volume of the canal = 5.5 * 4 * 405 = 22 * 405
Time = half an hour = 0.5 hrs

Rate * Time = Work 
=> 600R * 0.5 = 22 * 405
=> R = 22 * 405 / (0.5 * 600) = 22 * 405 / 300

Then how long a canal will 2500 men working for 6 hrs, dig if it is 10 m wide and 8 m deep? 
Rate of 2500 men = 2500 * R = 2500 * 22 * 405 / 300 = 25 * 22 * 135
Let Length of the canal = L
=> Work = Volume = L * 10 * 8

Rate * Time = Work 
=> 25 * 22 * 135 * 6 = L * 10 * 8
=> L = 25 * 22 * 135 * 6 / (10 * 8) = 5 * 11 * 135 * 3 / 4 = 5568.75 = 5568 3/4

So,  Answer will be B 
Hope it Helps!

Watch following video to MASTER Work Rate Problems

https://www.youtube.com/watch?v=dRxzi_x3ZwY

piermacabj · Answer

If 600 men can dig a hole (5.5 m wide, 4 m deep and 405 m long) in 0.5 hours that means this job can be finished en 6 hours by 50 men (600/12 = 50)

Now they ask you about what 2500 men can do in 6 hours so since 50 can dig (5.5*4*405) to know what 2500 can dig you multiply 50 to the previous work so you end with 5.5*4*405*50 = 445500 (which you could treat as the the "product" of this job)

Since they give you different measures in width a depth (10 and 8) you form a equation replacing this values and still equaling this new equation to the same "product" since 2500 men should always produce the same, so you end with:

x = long

10*8*x = 445500 
x = 445500/80

So you end with x (long) resulting in 5568.75, hence alternative B is the answer.

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