A wall clock loses 10 minutes every 1 hour. In 1 hour by the wall clock, a…

A chained-clock-rate problem: each clock's speed is defined relative to the PREVIOUS clock in the chain, not to true time directly. If clock B shows b minutes for every a minutes clock A shows, then over any interval, B's elapsed reading = A's elapsed reading x (b / a). When several clocks are chained this way, the overall conversion from true elapsed time to the LAST clock's reading is the PRODUCT of every stage's own rate ratio.

1. From noon to 6 p.m., true (real) time elapsed = 6 hours = 360 minutes.

2. Wall clock vs real time: it loses 10 min every real hour, so it shows only 50 min for every 60 real min, ratio = 50/60 = 5/6. Wall clock elapsed = 360 x 5/6 = 300 min = 5 h 00 min, i.e. it reads 5:00 pm.

3. Table clock vs wall clock: for every 60 min the wall clock shows, the table clock shows 70 min (10 min ahead), ratio = 70/60 = 7/6. Table clock elapsed = 300 x 7/6 = 350 min = 5 h 50 min, i.e. it reads 5:50 pm.

4. Alarm clock vs table clock: for every 60 min the table clock shows, the alarm clock shows only 55 min (5 min behind), ratio = 55/60 = 11/12. Alarm clock elapsed = 350 x 11/12 = 320.83 min = 5 h 20.83 min, i.e. it reads about 5:21 pm.

5. Wristwatch vs alarm clock: for every 60 min the alarm clock shows, the wristwatch shows 65 min (5 min ahead), ratio = 65/60 = 13/12. Wristwatch elapsed = 320.83 x 13/12 = 347.57 min = 5 h 47.57 min.

Cross-check by combining all four stage ratios into a single overall factor: (5/6) x (7/6) x (11/12) x (13/12) = 5005/5184 = 0.9656. Applying this once to the full 360 minutes gives 360 x 0.9656 = 347.57 minutes, matching the step-by-step chain and confirming the working.

So the wristwatch's elapsed reading is 347.57 minutes past noon, i.e. about 5 hours 47½ minutes. Of the four offered times only 5:47 pm lies anywhere near this value — the other three each correspond to a specific chaining error — so, to the nearest offered minute, the wristwatch shows 5:47 pm.