Question

Ramu purchased a second hand Swiss watch which is very costly. In this watch the minute-hand 3 and hour hand coincide after every $16\frac{3}{11}$ minutes. How much time does the watch lose or gain per day?

• A. $4$ min
• B. $5$ min
• C. $4$ min, $20$ sec
• D. None of these

Answer 1

Answer: (D)

None of these

The answer is option $D$

Degrees covered by hour hand in an hour $={360}^o$

$\Rightarrow$Velocity of hour hand $=360/60=6^o/min$

Degrees covered by minute hand in an hour $={30}^o$

$\Rightarrow$Velocity of hour hand $=30/60={0.5}^o/min$

Relative velocity of minute hand wrt hour hand $=6-0.5={5.5}^o/min$

In a proper clock, for the minute and hour hand to coincide when the hour hand is at $3$, the degrees that need to be covered wrt each other $={90}^o$

Time taken by a proper watch to cover ${90}^o$ by the minute hand wrt hour hand $=90/5.5=16.3mins=981$ secs

Time taken by the Swiss watch to cover the same degrees $=16\frac{3}{11}mins=16.27$ mins $=976$ secs

$\therefore$ Time gained by the swiss watch in $981secs=981-976=5secs$

Total time gained in a day (with $24\times 60\times 60$ secs $=86400$ secs) $=\frac{86400}{981}\times 5=440$ secs $=7$ mins $20$ secs