If 8 men working 9 hours a day can build a wall 18 metres long, 2 metr

Asked: If 8 men working 9 hours a day can build a wall 18 metres long, 2 metres wide and 12 metres high in 10 days, how many men will be required to build a wall 32 metres long, 3 metres wide and 9 metres high by working 6 hours a day in 8 days?

8*9*10 man-hours are required to build a wall 18*12*2 m^3
Number of man required to build a wall 32*9*3 m^3 = 32*9*3*10*9*8/18*12*2*6*8 = 30

IMO A

Bunuel

Why we took volume of the wall into consideration instead of just length and height?

LEARNING: (Men1 × time1) ÷ work1 = (men2 × time2) ÷ work2

(10 × 9hrs × 10days) ÷ (18 × 2 × 12) = (men2 × 6hrs × 8days) ÷ (32 × 3 × 9)

Uplon solving we get men2 = 30.

(A)

Why does this formula work?[B]

If 1 man takes 24hrs to pain 1 floor.
Then
(1) 2 Men will take 24hrs to paint 2 floors.
(2) 1 man sill take 48 hrs to paint 2 floors.

[B]notice as number of men increases (keeping time constant) the work doubls.

(a) Thus Men D.P work {D.P - directly proportional)

Similarly, keeping men same the time taken doubles to complete double the work.

(b) Thus, time D.P work.


From (a) and (b) we get

Men × time = D.P work.
Men × time = Work × K ( k is constant)

So,(Men × time) ÷ work = K

Thus,
(M1×T1)÷work1 = (M2×T2)÷work2 and so on...

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Total wall built by 8 men= 432 (VOLUME)
Total wall required to be built = 864 (volume)

Double the volume is needed.

8 men * 9 hrs * 10 days * 2 = X men * 6 hrs * 8 days
X= 8*9*10*2 / 6* 8 = 30

I guess because we don't know the width of one brick. If it is 2m wide then there was no need to calculate the volume initially. But if it were 1m wide then they must've built two standing layers of walls so the time invested in building the second standing layer of wall should be taken into consideration.

That's why the entire work done is the volume of the entire wall. IMO.

Thank you

Posted from my mobile device

8 men working 9 hours for 10 days to build a wall with volume of 432.
It follows that 8*9*10=720 man hours for 432 m^3
The wall to be built is 864 m^3 (I.e 432*2) therefore it will need 1440 man hours. Since the wall is going to be built in 8 days, it follows that the workers will need to work for (1440/8) 180 hours per day.
X men will be working for 180/6 hours a day => 30 men.

Answer is A

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CONCEPT: Time and Work
-The work here is constructing the wall with the given dimensions
-M1D1H1/L1B1H1 =M2D2H2/L2B2H2; [ M, D, H represent number of men, days & hours invested in a day respectively,;
L, B, H represent the length breadth and height as the dimensions of the wall respectively.]

SOLUTION: According to the concept discussed above we have
8*10*9/18*2*12 = M2*8*6/32*3*9
On solving, M2=30

Hope this helps. Keep studying!
Devmitra Sen

Don't see the wall as whole but lets build it the from scratch.
Assuming 1 meter is standard of measurement of the square bricks used to make the wall.

Length of wall - 18 meter - Lets call it 1st line of bricks each 1 meter in length. You can see 18 bricks lying on the ground in a straight line.

So , if someone asks whats the work done ; we are going to count the effort the only line that is 18.(1)


Width of wall - 2 meter - try to visualize we are putting 2nd line of bricks parallel to 1st line. So we have two rows of 18 bricks in front of us.

We could have width x meter - Similarly we have to put X line of bricks parallel to 1st line.

So , if someone asks whats the work done ; we are going to count the effort for each line. (2)

for first line - 18 bricks - 18 meter
for second line - 18 bricks - 18 meter

In this case it will be 18*2 or in general it will be "Width time Length"

Similarly , once we are done with line , lets do with the height.

Height of wall - 12 meter - We need to make 11 layers on top of the 1 layer of lines.

So , Now if someone asks whats the work done ; we are going to count the effort for each layer.(3)
for 1 layer it will be 18*2*1 (Length*Width*height)
for 12 layers it will be 18*2*12

Its easier to call the effort/Work mentioned here (1), (2) and (3) as Volume(LBH)

Hence, we are taking Volume as Work Done