In alloys A and B, the ratio of lead to tin is 5 : 3 and 3 : 1, respectively. 80 kg of alloy A and 100 kg of alloy B are mixed together to form a new alloy. What is the amount of tin (in kg) in the new alloy?

To find the total amount of tin in the new alloy, we need to calculate the amount of tin contributed by each of the two alloys, A and B, individually, and then sum them up.

Step 1: Calculate the amount of tin in alloy A
In alloy A, the ratio of lead to tin is given as $5:3$.
This means that for every $5+3=8$ parts of alloy A, $3$ parts are tin.
So, the fraction of tin in alloy A is:
$\frac{3}{8}$
Given that the total mass of alloy A is $80\text{kg}$, the amount of tin in alloy A is:
$\text{Tin in A}=80\times \frac{3}{8}=10\times 3=30\text{kg}$

Step 2: Calculate the amount of tin in alloy B
In alloy B, the ratio of lead to tin is given as $3:1$.
This means that for every $3+1=4$ parts of alloy B, $1$ part is tin.
So, the fraction of tin in alloy B is:
$\frac{1}{4}$
Given that the total mass of alloy B is $100\text{kg}$, the amount of tin in alloy B is:
$\text{Tin in B}=100\times \frac{1}{4}=25\text{kg}$

Step 3: Calculate the total amount of tin in the new mixture
The new alloy is formed by mixing $80\text{kg}$ of alloy A and $100\text{kg}$ of alloy B.
The total amount of tin in the new alloy is the sum of the tin from both alloys:
$\text{Total Tin}=\text{Tin in A}+\text{Tin in B}$

Therefore, the amount of tin in the new alloy is $55\text{kg}$, which corresponds to Option 55.