Question

A clock is at the right time at 8:00 am. The clock gains 10 minutes in 24 hours. What will be the correct time when the clock shows 1:00 pm on the following day?

• A. 12:05 pm
• B. 12:35 pm
• C. 12:48 pm
• D. 12:55 pm

Hint:

For gaining clocks: \[ \text{Actual Time} = \text{Clock Time}\times \frac{\text{Actual Day}}{\text{Clock Day}} \]

Answer 1

The Correct Option is D

Concept: A clock gaining 10 minutes in 24 hours means \[ 24\text{ hours actual} = 24\text{ h }10\text{ min clock time} \] \[ 1440\text{ min actual}=1450\text{ min clock} \]

Step 1: Determine the displayed elapsed time. From 8:00 am to 1:00 pm next day: \[ 24+5=29\text{ hours} \] Clock shows elapsed time \[ 29\times60=1740\text{ minutes} \]

Step 2: Find actual elapsed time. \[ \text{Actual elapsed} = 1740\times\frac{1440}{1450} \] \[ =1728\text{ minutes} \] \[ =28\text{ h }48\text{ min} \]

Step 3: Add to the starting time. Starting time: \[ 8:00\text{ am} \] Adding \(28\) h \(48\) min: \[ 12:48\text{ pm} \] Thus the correct time is \[ \boxed{12:48\text{ pm}} \]