Question

A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is:

• A. \(59 \tfrac{7}{12}\) min. past 3
• B. 4 p.m.
• C. \(58 \tfrac{7}{11}\) min. past 3
• D. \(2 \tfrac{3}{11}\) min. past 4

Hint:

Set up the ratio \(\text{watch}:\text{real}=37:36\) for a watch gaining \(5\) s per \(3\) min; multiply the shown interval by \(\tfrac{36}{37}\).

Answer 1

The Correct Option is B

Step 1: The watch gains \(5\) s every \(3\) min, i.e. \(100\) s every real hour, so watch time \(=\) real time \(\times\dfrac{37}{36}\).

Step 2: The watch shows \(9\) h \(15\) min \(=9.25\) h elapsed since \(7\) a.m., so real hours \(R=9.25\times\dfrac{36}{37}\).

Step 3: Simplify: \(R=\dfrac{333}{37}=9\) hours; adding this to \(7\) a.m. gives the true time.
\[ \boxed{4\ \text{p.m.}} \]