When I get multiplied by any number, the sum of the figures in the product is always me. What am I?

A famous swimmer can swim downstream in a lake in exactly 40 minutes with the lake current.
He can swim upstream in that lake in exactly 60 minutes against the lake current.
The length of the lake is 2 km.

How long he can cover the distance of one side at a still lake with no current?

Sherlock Holmes was challenged to make a pre-drawn line smaller without erasing it. He did it in fractions of seconds. How?

Christina is practising her dance steps along with her friends. In a particular sequence, all of them form a row. At that point, Niharika is standing in the 4th position from either end of the row.
Can you find out how many girls are practising together?

What has one letter and starts with an E?

John has played 50 ODI's and his average is 50. How many runs should he score in his 51st ODI, so that his average score jumps to 51?

Rectify the following equality 101 - 102 = 1 by moving just one digit.

Once upon a time, there was a castle on a square island. The entire island was surrounded by a 14m wide trench. The Romans had wanted to invade the castle and had brought a few wooden planks along with them to facilitate themselves in crossing the moat. The planks were however found to be only 13m long.

The Romans still managed to cross the trench. How did they do it?

How many pluses should we put between the digits of 987654321 to get a total of 99, and where?

Next Number in the Series,

5, 16, 49, 104, ?