1. Statement of the problem: A ship has a draft at the LCF of $8.0 m$ and a trim by the stern of $0.6 m$. A mass of $200 t$ is added $30 m$ aft of the LCF. Given $Delta = 14000 t$, TPC = $16.4 t/cm$, MCT1cm = $17 t-m/cm$, and LCF at midships, determine the new trim and the new draft at the LCF. 2. Compute the trimming moment caused by the added mass about the LCF. $M = 200*30 = 6000$ t-m. 3. Compute the change in mean draft caused by the added weight using TPC. $d_{mean} = 200/16.4 = 12.1951219512$ cm = $0.1219512195$ m. 4. Compute the change in trim caused by the trimming moment using MCT1cm. $trim_{change} = 6000/17 = 352.9411764706$ cm = $3.529411764706$ m. 5. Update the ship's trim and the draft at the LCF. New trim = $0.6 + 3.529411764706 = 4.129411764706$ m. New draft at LCF = $8.0 + 0.1219512195 = 8.1219512195$ m. 6. Final answer: The new trim by the stern is $4.129411764706 m$ and the new draft at the LCF is $8.1219512195 m$.