Solution:

Were you thinking of using the fastest person who takes one minute to travel to and fro till everyone has reached the other end? Yes that can be done but it will take 10 + 1 + 7 + 1 + 2 = 21 minutes in total.

If we pay attention towards finding a way to merge the one taking 7 minutes and the one taking 10 minutes, we will have to acknowledge the fact that one of them will also have to return back which will take much more time than 21 minutes.

What if we use the person taking 2 minutes to escort the one taking 1 minutes across? Let's come to the conclusion:

1 and 2 cross the bridge
2 returns with the torch
7 and 10 cross the bridge
1 comes back
1 and 2 cross the bridge

In such a manner, the total time taken will be
2 + 2 + 10 + 1 + 2 = 17 minutes.

Solution:

This series can be quite tricky at first glance so look closely. It is almost the same number only, the lowest digit of the previous one is missing from the next.

Thus the next after 975 will be 97 as 5 is the lowest digit.

Solution:

This is quite an easy question which is used generally as a warm up question during the interviews.

It is true that only three points are equidistant from each other. But take a paper and draw four points in the shape of a pyramid. You can definitely draw four equidistant points. Thus all you have to do as a builder is build the buildings in the same manner. In this way, one building will be placed in between the three buildings.

Solution:

This problem might sound confusing but for the solution, all you have to do is take the LCM of 4, 8, 6 and 10 which is 120 min or 2 hours.

Thus the bells will toll again when the clock strikes 2 am + 2 = 4 am.

Solution:

The worst case will be when you don't take out three pairs of same color will be that you take out 2 red, 4 yellow and 5 of each color. In that manner, you will have to take out 46 socks. But if you take out one more sock, you will have 6 socks of at least one color. Thus in that case, you must take out 47 socks to make sure that you have taken out at least three pairs of same color socks.