The watch which gains uniformly is 2 mins. slow at noon on...

The watch which gains uniformly is 2 mins. slow at noon on Sunday and is $4 \mathrm{~min}$. 48 secs. fast at 2 p.m. on the following Sunday. The watch was correct at
(a) 2 p.m. on Tuesday
(b) 12 noon on Monday
(c) 1:30 p.m. on Tuesday
(d) $12: 45$ p.m. on Monday

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Key Concepts

Time Interval Computation

This involves calculating the duration between the two known reference times. By assessing how much total error change occurs over the full time period, one can proportionally determine the exact instance within that interval when the watch was correct.

Linear Interpolation

Since the watch’s error changes uniformly, linear interpolation is applied to estimate the time at which the watch would display correctly. This involves using the two known error points to determine when the accumulated error would be zero.

Uniform Time Gain

This concept refers to a scenario where a timekeeping device gains time at a constant rate. It implies that the error in the watch’s time increases linearly with time, allowing one to predict the watch's error at any given moment using simple proportional reasoning.

Rate Calculation

Rate calculation involves determining the amount of time gained per unit of time. By knowing the watch’s error at two different times, one can calculate the incremental gain per minute or hour, which is crucial for tracking how the error develops over time.

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