Question

Rajeev's watch gains 1 minute in an hour and Sanjeev's watch loses 2 minutes in an hour. Once they set both the watches at 12 : 00 noon. When will the two incorrect watches of Rajeev and Sanjeev show the same time together ?

• A. 8 days later
• B. 10 days later
• C. 6 days later
• D. can't be determined

Answer 1

The correct option is B 10 days later

Rajeev's watch gains $1min$ in an hour

$\Rightarrow$ Speed of Rajeev's watch $=61min/hr$

Sanjeev's watch loses $2min$ in an hour

$\Rightarrow$ Speed of Sanjeev's watch $=58min/hr$

Relative velocity of Rajeev's watch wrt Sanjeev's watch =$(61-58)=3min/hr$

To show the same time wrt to each other the Rajeev's watch has to make up $12$ hrs wrt to Sanjeev's watch

Time take to make up this $12$ hrs (or $12\times 60$ min) $=(12\times \frac{60}{3})=12\times 20$ hrs $=24\times 10$ hrs $=10days$

The answer is option $B$.