Question

In a car park the ratio of red cars to green is 5:6 while that of green cars to blue is 3:10 find the ratio of red cars to green cars to blue cars in its simplest form

Answer 1

5:6::10:3
15:60
1:4
Since in the 1st case the green was mentioned after red and in the 2nd cas green was mentioned 2nd.
So that's why 3:10 was taken as inverse proportion

Answer 2

Red: Green = 5:6 
Green: Blue = 3: 10 

To get a common ratio for all the 3 objects 
you need to get the comman object(green) have the same ratio value in both the equation 
For this you need to take the LCM of the ratio values of green ie 6 and 3 
the LCM of 6 and 3 is 6 itself 
So to get 6 in the first equation 
you need to multiply it by 1 
ie 5*1 : 6*1 Here for the ratio to remain the same you need to multiply 5*1 
ie 5:6 

Now in the second equation green is 3 
to get 6 multiply it by 2 
ie 3*2:10*2 Here for the ratio to remain the same you need to multiply 10*2 
the equation becomes 
6:20 
Now since the equations have a comman value of green they can be put together 

ie 5:6:20 

Now since they are in order we can take the ratio of Red and Blue directly 
ie 5:20 
Which when simplified is 
1:4