On 16 June in DR position LAT 50°57.0'S, LONG 53°03.9'W (ZD+4), you take an ex-meridian observation of Acrux at lower transit. The chronometer time of the sight is 10h 08m 18s, and the chronometer error is 02m 12s fast. The sextant altitude (hs) is 23°49.0'. The index error is 1.1' off the arc, and your height of eye is 26 feet. What is the latitude at meridian transit?

Correct Answer: Option D — 50°41.2'S

Applying Bowditch procedures for ex-meridian observations, calculate the time difference from transit and the reduction factor. After correcting the sextant altitude for index error, dip, and refraction, apply the reduction to the observed altitude. The resulting latitude at transit is 50°41.2'S, consistent with the celestial intercept method.