Question

A clock loses 2 minutes in a hour and another clock gains 2 minutes in every 2 hours. Both these clocks are set correctly at a certain time on Sunday and both the clocks stop simultaneously on the next day with the time shown being 9 am and 10 : 06 AM. What is the correct time at which they stopped?

• A. 9 : 54 am
• B. 9 : 44 pm
• C. 9 : 46 am
• D. 9 : 44 am

Answer 1

The correct option is D 9 : 44 am

The answer is option $D$

Speed of $1^{st}$ clock $=58min/hr$

Speed of $2^{nd}$ clock $=61min/hr$ [Since it gains $2min$ in $2hrs$, it should gain $1min$ in $1hr$]

Relative velocity of $2^{nd}$ clock wrt $1^{st}=61-58=3min/hr$

Relative distance travelled by the $2^{nd}$ clock wrt $1^{st}$ by the time both are stopped $=1hr6min=66min$

Time taken by the $2^{nd}$ clock wrt $1^{st}$ to cover $66min=66/3=22hours$

In those $22$ hours, mins covered by the $1^{st}$ clock $=22\times 58=1276$

The actual mins elapsed in those $22hours=22\times 60=1320$

$\therefore$ Number of mins the $1^{st}$ clcok is behind the correct time$=1320-1276=44mins$

$\Rightarrow$ If the time on the $1^{st}$ clock is $9am$, then the correct time is $9:44am$