Question

One watch is $1$ minute slow at $1$ pm on Tuesday and $2$ minutes fast at $1$ am on Friday. When did it show that correct time?

• A. $5.00$ am on Wednesday
• B. $9.00$ am on Wednesday
• C. $5.00$ pm on Wednesday
• D. $9.00$ pm on Wednesday

Answer 1

The correct option is B $9.00$ am on Wednesday

It takes $24\times 2+12=60$ hours from 1 pm of Tuesday to 1 am of Friday i.e. $60\times 60=3600$ minutes.

So, in real $3600$ minutes it counts $3600+1+2=3603$ minutes(1 minute slow at 1 pm on Tuesday and 2 minutes fast at 1 am on Friday).

So, in one real minute it counts $3603/3600=1.0008333$ minutes.

Suppose, after x minutes from 1 pm on Tuesday, it'll show the correct time.

Then, real x minutes=(x+1) minutes in the given watch.

$⟹$ 1 minute=(x+1)/x minutes in the given watch.

$⟹$ $(x+1)/x=1.0008333$

$⟹$ $x+1=1.0008333x$

$⟹$ $x=1/0.0008333=1200.048$ min $=20.0008$ hrs

$\therefore$ 1 pm on Tuesday + 20 hrs = 9 am on Wednesday.

Hence, the watch will show correct time at $9:00$ am on Wednesday.