Distance Between Houses?

Four friends built a colony for themselves. They built their own houses at different
distances from each other.

Chris lived 60 km away from Alex.
Darren lived 40 km away from Bill.
Chris lived 10 km nearer to Darren than he lived to Bill.

Can you find out how far was Darren's house from Alex?

Click here to know the distance! 

Locations of 4 Friends

What was the given data & question? 

Let's represent houses of friends by their initial letter of the name i.e. C is the house of Chris, D is the house of Darren, B is Bill's house & A is name of Alex's house.

Now C & A are located at 60 km away from each other while D & B are 40 km apart i.e. CA = 60 & DB = 40.

As per given data, D is 10 km nearer than B from C. Hence, CB = CD + 10

There are 5 possibilities of the locations of these 4 friends.

Case 1. D & B are in between C & A.

In this case, 

CD + DB + BA = 60

but DB = 40,

CD + BA = 20,

CB - 10 + BA = 20

CB + BA = 30 i.e. CA = 30

But CA = 60, hence this combination is not possible. Other way, CB >= 40, since CD = CB-10, CD >= 30. That means CD + DB >= 70 for which B needs to be beyond A as CA = 60.

Case 2 : A is between D & B.

In this case, CD + DA  = 60, DA + AB = 40 . If we subtract second one from first, we get,

CD - AB = 20

CB - 10 - AB = 20

CB - AB = 30  

CA = 30 but CA = 60. Hence, this combination too is invalid.