The average weight of $A,B$ and $C$ is $60\text{kg}$. If the average weight of $A$ and $B$ is $30\text{kg}$ and that of $B$ and $C$ is $70\text{kg}$, then what is the weight of $B$?

Let the individual weights of $A,B,$ and $C$ be represented by $A,B,$ and $C$ respectively.
**Step 1: Express total sum of $A,B,$ and $C$ **

$$\frac{A+B+C}{3}=60⟹A+B+C=60\times 3=180\text{kg}\text{— (Equation 1)}$$

**Step 2: Express total sum of $A$ and $B$ **

$$\frac{A+B}{2}=30⟹A+B=30\times 2=60\text{kg}\text{— (Equation 2)}$$

**Step 3: Express total sum of $B$ and $C$ **

$$\frac{B+C}{2}=70⟹B+C=70\times 2=140\text{kg}\text{— (Equation 3)}$$

**Step 4: Solve for $B$ **
Add Equation 2 and Equation 3 together:

$$(A+B)+(B+C)=60+140$$

$$A+2B+C=200\text{kg}$$

We can rewrite this expression as:

$$(A+B+C)+B=200$$

Substitute the value of $(A+B+C)$ from Equation 1 into this expression:

$$180+B=200$$

$$B=200-180=20\text{kg}$$

Thus, the weight of $B$ is $20\text{kg}$.