Question

Each day on Planet M is 10 hours, each hour 60 minutes and each minute 40 seconds. The inhabitants use a 10-hour analog clock. If such a clock shows \(\,3\) hours \(42\) minutes \(20\) seconds in a {mirror, what will be the time on Planet M exactly after \(5\) minutes?}

• A. 6 hours 18 minutes 20 seconds
• B. 6 hours 22 minutes 20 seconds
• C. 6 hours 23 minutes 20 seconds
• D. 7 hours 17 minutes 20 seconds
• E. 7 hours 23 minutes 20 seconds

Hint:

For mirror times on an \(N\)-hour analog clock, use \(\text{actual} = N{:}00{:}00 - \text{mirror}\). When units are unusual (here \(1\) min \(=40\) s), convert to the smallest unit, subtract, then reconvert.

Answer 1

The Correct Option is B

Step 1: Convert mirror reading to actual time.
On an analog dial, the mirror time equals \(\text{dial period} - \text{actual time}\). Here the dial period is \(10{:}00{:}00\) (i.e., \(10\) hours). So, \[ \text{Actual time} \;=\; 10{:}00{:}00 - 3{:}42{:}20. \] Work in Planet-M seconds (1 min \(=40\) s, 1 hr \(=60\times 40=2400\) s):
\(10{:}00{:}00 = 10\times 2400 = 24000\) s, \quad \(3{:}42{:}20 = 3\times 2400 + 42\times 40 + 20 = 8900\) s.
Thus, \[ 24000 - 8900 = 15100\ \text{s} \Rightarrow 6\ \text{hrs}\; 17\ \text{mins}\; 20\ \text{s}. \] Step 2: Add 5 Planet-M minutes.
\(5\) minutes \(= 5\times 40 = 200\) s. \(15100 + 200 = 15300\) s \(\Rightarrow\) \(6\) hrs \(22\) mins \(20\) s. \[ \boxed{\text{Time after 5 minutes }=\ 6\ \text{hours}\ 22\ \text{minutes}\ 20\ \text{seconds}} \]