Let $ABCDV$ be a regular quadrangular pyramid with $V$ as the apex. The plane $\lambda$ intersects the $VA$, $VB$, $VC$ and $VD$ at $M$, $N$, $P$, $Q$ respectively. Find $VQ : QD$, if $VM : MA = 2 : 1$, $VN : NB = 1 : 1$ and $VP : PC = 1 : 2$.
1. **Define the problem and given ratios:**
   - We have a regular quadrangular pyramid \(ABCDV\) with \(V\) as the apex.
   - The plane \(\lambda\) intersects \(VA\), \(VB\), \(VC\), and \(VD\) at \(M\), \(N\), \(P\), and \(Q\) respectively.
   - Given ratios are:
     \[
     \frac{VM}{MA} = 2:1, \quad \frac{VN}{NB} = 1:1, \quad \frac{VP}{PC} = 1:2
     \]

2. **Assign lengths based on given ratios:**
   - Let the length of \(VA = a\).
   - From \(\frac{VM}{MA} = 2:1\), we have \(VM = \frac{2}{3}a\) and \(MA = \frac{1}{3}a\).
   - Let the length of \(VB = b\).
   - From \(\frac{VN}{NB} = 1:1\), we have \(VN = \frac{1}{2}b\) and \(NB = \frac{1}{2}b\).
   - Let the length of \(VC = c\).
   - From \(\frac{VP}{PC} = 1:2\), we have \(VP = \frac{1}{3}c\) and \(PC = \frac{2}{3}c\).

3. **Assume the pyramid is regular:**
   - Since the pyramid is regular, all the slant heights \(VA\), \(VB\), \(VC\), and \(VD\) are equal. Let this common length be \(s\).
   - Therefore, \(a = b = c = d = s\).

4. **Calculate the coordinates of intersection points:**
   - Let \(V\) be at the origin \((0,0,0)\).
   - Let \(A\), \(B\), \(C\), and \(D\) be at the base of the pyramid in the \(xy\)-plane.
   - The coordinates of \(M\), \(N\), \(P\), and \(Q\) can be determined using the given ratios:
     \[
     M = \left(0, 0, \frac{2}{3}s\right), \quad N = \left(0, 0, \frac{1}{2}s\right), \quad P = \left(0, 0, \frac{1}{3}s\right), \quad Q = \left(0, 0, q\right)
     \]

5. **Determine the ratio \(VQ : QD\):**
   - Since \(Q\) lies on \(VD\), we need to find the ratio \(\frac{VQ}{QD}\).
   - Let \(VQ = x\) and \(QD = s - x\).
   - Given the symmetry and the regularity of the pyramid, we can use the fact that the plane \(\lambda\) intersects the slant heights proportionally.
   - From the given ratios, we can infer that the plane \(\lambda\) divides the slant heights in a consistent manner.

6. **Calculate the exact ratio:**
   - Using the given ratios and the fact that the pyramid is regular, we can set up the proportion:
     \[
     \frac{VM}{MA} = \frac{VN}{NB} = \frac{VP}{PC} = \frac{VQ}{QD}
     \]
   - From \(\frac{VM}{MA} = 2:1\), we have:
     \[
     \frac{VQ}{QD} = 2:1
     \]
   - Therefore, \(VQ = 2k\) and \(QD = k\) for some constant \(k\).

7. **Solve for the ratio:**
   - Adding these, we get:
     \[
     VQ + QD = 2k + k = 3k
     \]
   - Since \(VQ = 2k\) and \(QD = k\), the ratio is:
     \[
     \frac{VQ}{QD} = \frac{2k}{k} = 2
     \]

The final answer is \(\boxed{2:1}\).