GATE Mechanical 2019 Set 1 | GA | Question: 3

Question

A worker noticed that the hour hand on the factory clock had moved by $225$ degrees during her stay at the factory. For how long did she stay in the factory?

• A. $3.75$ hours
• B. $4$ hours and $15$ mins
• C. $8.5$ hours
• D. $7.5$ hours

Comments

In this type of questions it should be clearly mentioned whether the clock is in 12-hrs format or 24-hrs. format.

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by default we can take 12 hr format right ?

Answer 1

Hour hand of a clock covers $360^{\circ}$ in $12$ hours.

Since, $360^{\circ}$ is covered in $12$ hours. So, $225^{\circ}$ will be covered in $\frac{225^{\circ}}{360^{\circ}}\times12 = 7.5$ hours.

So, Answer is (D)

Answer 2

Number of hours in a clock $= 12$ hours

One rotation hour hand covers $360^{\circ} $

$360$ degrees $= 12$ hours

$1$ degree $=\dfrac{12}{360}$ hours

$225$ degrees $=\dfrac{12}{360}\times 225$ hours $=7.5$ hours

                                                                                    $(OR)$

The worker stays in the factory $=3\ hours \ ({0^{\circ} \ to \ \ 90^{\circ}}) +3 \ hours  \ ({90^{\circ} \ to \ \ 180^{\circ}}) +\dfrac{3}{2}\ hours \ ({180^{\circ} \ to \ \ 225^{\circ}}) = 7.5 \ hours$

So, option $(D)$ is the correct choice.

Answer 3

Hour clock moves 360°  in 12 hrs

 

=> in 1°  movement of hour clock time passed =  12/360  hrs

= 1/30 hrs

in 225°  movement of  hour clock time has passed = 225/30 hrs

= 15/2  hrs

= 7.5 hrs

 

She stayed for 7.5 hrs in factory if factory clock had moved by 225 ° during her stay

Answer 4

For 1 hour the hour hand takes 30 deg.

Therefore 225 deg / 30 deg = 7.5 hours.