Your question:
The ratio of bananas to apples is 3:4 and the ratio of apples to tomatoes is 2:5. Find the ratio of bananas to tomatoes.

Ans:
Bananas to apples (call it B:A) = 3:4 
Apples to tomatoes (call it A:T) = 2:5

Since the common fruit is apple, we need to convert the number of apples to be
the same in both the cases.

B:A = 3:4
A:T = 2:5 which is the same as 4:10  (if 2 apples gets you 5 tomatoes, then
4 apples will get you 10 - since 4 = 2*2)

In simple terms, for every 3 bananas you get 4 apples. For every 4 apples you 
get 10 tomatoes. So for every 3 bananas you get 10 tomatoes.

Ratio of Bananas to Tomatoes = 3:10

:)