Proportion(quantitative analysis doubt)

I searched the web.

Found this..

if A:B=a:b and B:C=c:d than A:B:C is ac:bc:bd

Hence i get the correct answer.

But now i am unable to find the logic to above conclusion.In sense how was the formula derived ?

Anyone got the logic  ?

Since the ratio's are representing 3 terms......inorder to get a common ratio you've to get the common variable in both the ratios equal so that it corresponds in given proportion to the other two variables involved......

Here since B is common in both by multiplying with some no. it is made equal in both ratios......and correspondingly in order to satisfy with the ratio's you multiply the same no for other involved(that becomes 3 or c in first ratio and 2 or b in the second ratio.......

Thanks swetha now i got the logic.thanks again

Next doubt question 25 page 21 indices.

Idea how to solve it?