Question

A watch, which gains uniformly, is 3 minutes slow at noon on Monday and is 3 minutes 48 seconds fast at 2 p.m. on the following Monday. What time it was correct ?

• A. 2 p.m. On Tuesday
• B. 2 p.m. On Wednesday
• C. 3 p.m. On Thursday
• D. 1 p.m. On Friday.

Answer 1

The correct option is C 3 p.m. On Thursday

Watch is $3$ minutes slow at noon on Monday.
Watch is $3$ minutes $48$ second fast at $2$ pm on next Monday.
Time period $=7$ days $2$ hours $=168+2=170$ hours.
Watch that was earlier $3$ minutes slow becomes $3$ minutes $48$sec. fast
$\therefore$ Gap between it is $6$ minutes $48$ sec $=408$ sec.
Change in time in $170$ hours $=408$ sec.
Change in time in $1$ hour $\frac{408}{170}=2.4$ sec.
Time will be correct when it moves $3$ minutes.
$2.4$ second $\times$ number of hours $=3$ minutes ($180$ second)
Number of hours $\frac{180}{24}\times 10=75$ hours ($3$ days $3$ hours)
$\therefore$ After 3 days 3 hours from Monday noon, the watch will show correct time.
$\therefore$ $3$ pm. on Thursday.