In triangle ABC, D is a point on BC such that BD : DC = 3 : 4. E is a point on AD such that AE : ED = 2 : 3. Find the ratio area (ΔECD) : area (ΔAEB).

2 : 1

\(\frac{Area\; of \; AEB}{Area\;of\;EBD}\) = \(\frac{2}{3}\)    ...(1)

\(\frac{Area\; of \; EBD}{Area\;of\;ECD}\) = \(\frac{3}{4}\)   ..(2)

From eq (1) and (2), we have

\(\Delta \)AEB : \(\Delta \)EBD : \(\Delta \)ECD

        2     :      3      :        4

Now,

\(\frac{Area\; of \; ECD}{Area\;of\;AEB}\) = \(\frac{4}{2}\) = \(\frac{2}{1}\)= 2 : 1

Therefore, the required ratio is 2 : 1.