Solution:

If you are thinking of how to cut in such a way that you are able to make seven equal pieces, you are thinking in the wrong direction. You should give more stress on how to make the transaction with the worker.

You have to break the gold bar two times so you have the following sizes of the bar:

1/7 ---- Bar A
2/7 ---- Bar B
4/7 ---- Bar C

When the day 1 ends:
Give Bar A (You remain with Bar B and Bar C; Worker possess - Bar A)

When the day 2 ends:
Give Bar B and take the Bar A back (You remain with Bar A and Bar C; Worker possess - Bar B)

When the day 3 ends:
Give Bar A (You remain with Bar C; Worker possess - Bar A and Bar B)

When the day 4 ends:
Give Bar C and take back Bar A and Bar B (You remain with Bar A and Bar B; Worker possess - Bar C)

When the day 5 ends:
Give Bar A (You remain with Bar B; Worker possess - Bar A and Bar C)

When the day 6 ends:
Give Bar B and take back Bar A (You remain with Bar A; Worker possess - Bar B and Bar C)

When the day 7 ends:
Give Bar A (You remain with no bar; Worker possess - Bar A, Bar B and Bar C)

Thus by the end of seven days, you have taken care of everything.

Solution:

Two men and seven women complete the work in four days
Or we can say that eight men and twenty eight women complete the work in one day

Also,
Four men and four women complete the work in three days
Or we can say that twelve men and twelve women complete the work in one day

Now we know that the work is same

8 men + 28 women = 12 men + 12 women
1 man = 4 women

Put it into any equation
Four men and four women complete the work in three days
Or four men and one man complete the work in three days
= Five men complete the work in three days
= One man complete the work in three*five = fifteen days

Solution:

Before moving forward with the solution do keep in mind that the answer is demanded in minutes.

Drops in the bucket = x
Time taken to leak z drops = t seconds
Time taken to leak one drop = t/z seconds

Time taken to drop x drops = (x.t)/z seconds
We must convert it into minutes for our final answer
So the minutes taken to leak x drops = (x.t) / (z.60)

Solution:

Calculate the LCM of 2, 4, 6, 8, 10 and 12 seconds.
The outcome will be 120 seconds.

Thus at 2 minutes, it rings once.

Which means that the bells will ring 15 times in the 30 minutes.

But wait that will be an incorrect answer as the bells will also ring together in the 0th second.

Which means the bells toll together 15 + 1 = 16 times.

Solution:

It will take 68 minutes to complete one round of the larger garden.

Let the width of the smaller garden (rectangle) be 4 units
Then the length of the smaller garden will be 6 as it is fifty percent more
The perimeter of the garden = 2(6 + 4) = 20 units

20 units are covered in 20 minutes (as per the question)
Which means that it takes 1 minute to cover 1 unit.

In the large garden as per the question,
Width = 16 units and length = 18 units
Thus the perimeter = 2(16 + 18) = 68 units.

According to what we analyzed above, it will take the person 68 minutes to complete one round of the big garden.

Solution:

58 minutes

If you see the net progress of the hiker, it is one feet per minute. The most common answer is therefore 60 minutes or an hour. But if you consider the situation, after 58 minutes, he would have climbed the mountain and would be on top of it, thus he will not slip back.

Solution:

120

Explanation:
Let g be the grass in the beginning
r be the rate at which grass grows everyday
y be the rate at which one cow eats the grass per day
n be the number of cows to eat the grass in 96 days

g + 40*r = 40*40*y ------- 1
g + 60*r = 30*60*y ------- 2
g + n*r = 20*n*y ---------- 3

from 1 and 2 we have
r = 10y and g = 120r
using 3, we get
nr=120r
n = 120

Solution:

Time : 3.21 hours

To solve the problem
(1/X) + (1/Y) = 1/T
After Solving
14/45 = 1/T
Thus T = 45/14 = 3.21

Solution:

25 seconds

Explanation:
Machine X manufactures 120/40 = 3 microchips every second
Machine Y produces 100/20 = 5 microchips per second
Combined productivity per second = 3 + 5 = 8
Hence seconds required to manufacture 200 bolts = 200/8 = 25 seconds

Solution:

18 Hours