Quantitative Aptitude question - 25 non-parallel lines in a plane, How many intersections?

Ques - There are 25 lines in a plane such that no two of them are parallel to each other, so how many intersections?

Ans - Now since no line is parallel to any other 24 lines, this means that every line is cut by the remaining 24 lines.

Hence, All 25 lines will be cut by the others, Hence  25x24=600.

But sometimes the question a little bit more twisted. Here it is.

Ques - There are 25 lines in a plane such that no two of them are parallel to each other and no 3 are concurrent to each other, so how many intersections?

Ans - Now since we know that 3 or more lines are said to be concurrent only if they intersect at one point.

Since according to the question no more than 3 lines can intersect at one point. Hence we have the following

Now from the above picture it is quite clear that one line would be cut down by 2 other lines at one point. Hence giving us the condition that only 3 intersect at single point.

Now we know from the above question that there were 24 different points of intersection on  the 25th line but in this case we will have only 12.

Hence 12 points on each of 25 lines.

Therefore answer =25x12 =300.