Four-digit number

For a four-digit number abcd, ab: bc = 1:3 and bc: cd = 2:1 (ab, bc, and cd are two-digit numbers from digits
a, b, c, d). Find this number(s).

Correct answer:

x₁ =  1421
x₂ =  2842

Step-by-step explanation:

$$\begin{gathered} x_1=1421 \\ a{b}_1=14 \\ b{c}_1=42 \\ c{d}_1=21 \\ {t}_{11}=3\cdot a{b}_1=3\cdot 14=42 \\ {t}_{21}=2\cdot c{d}_1=2\cdot 21=42 \\ {t}_{11}=t_{21}=b{c}_1 \end{gathered}$$

$$\begin{gathered} x_2=2842 \\ a{b}_2=28 \\ b{c}_2=84 \\ c{d}_2=42 \\ {t}_{12}=3\cdot a{b}_2=3\cdot 28=84 \\ {t}_{22}=2\cdot c{d}_2=2\cdot 42=84 \\ {t}_{12}=t_{22}=b{c}_2 \end{gathered}$$

Try another example