**Que 1: There are few bacteria in a bottle which gets double every day. On the 10th day, that bottle gets full. On which day the bottle was one-fourth.**

Ans 1: If the bacteria is double each day and on the 10^{th} day, the bottle is getting full it means, It was half on the 9th day and one-fourth on the 8^{th} day.

**Que 2: 100 coins are lying on a table. 10 of them are heads up and 90 are tails up. You can’t see and feel the coins. How can we split the coins into two piles such that there is the same number of heads up in each pile?**

Ans 2: We can make 2 piles of 10 and 90. Suppose if x coins are heads and 10-x tails on the 1st pile then it means there are 10-x heads are there in the 2nd pile. If we flip all the coins in 1st pile, then there will be 10-x heads up which will be equal to heads in 2^{nd} pile.

**Que 3: Four persons want to cross a bridge. They take 1min., 2min., 5min. and 10min. to cross the bridge respectively. If only two people can cross the bridge at a time and they need a torch. They have only one torch, so each time they cross they have to bring back that torch. Both the person crossing the bridge should have to walk together. In how much minimum time they all will cross the bridge?**

Ans 3: Suppose we have persons a, b, c, and d which take 1min., 2min, 5min. and 10min. to cross the bridge respectively. We will follow the following sequence :

a and b cross the bridge: 2min.

a will return back: 1min.

c and d cross the bridge: 10 min.

b will return back: 2min.

a and b cross the bridge: 2min.

So in total 17 min. they all will cross the bridge.

**Que 4: There are three closed boxes. There are apples in one box, oranges in 2nd box, and mixed fruit (apple and orange) in 3rd box. By mistakenly the labels of the items are incorrectly tagged on all the boxes. You can draw any one fruit from any box and label them correctly. ****Ans 4:** Pick a fruit from the basket labeled ‘Mix fruit’. We know from the question that this basket does not contain ‘Mix fruit’ in that box.

If this fruit is an apple, then label this Basket as ‘Apple’. Now we’ve determined that the basket labeled as ‘Mix fruit’ only contains Apples.

The basket labeled as ‘Oranges’, but we know that since the label is incorrect, this basket either has only apples in it or has Mix fruit. Since we already know which basket contains only apples, we know that the basket labeled as ‘Oranges’ contains ‘Mix fruit’. So label it as ‘Mix fruit’. The 3rd basket will be labeled as ‘Oranges’.

**Que 5: There are three persons at different places on a circular track, They start running in a random direction with the same speed, what is the probability that they will not cross each other?Ans 5: **Each person can run in two directions clockwise or anticlockwise. So, all the people will have 2 options. So there will be a total of 8 possibilities in which they can run. They won’t cross each other if they all run in the same direction clockwise or anticlockwise. So, In 2 cases out of 8, they will not cross, Probability will be 2/8 = ¼.

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