GATE Overflow Test Series | Mock GATE | Test 2 | Question: 7

Question

The angle between the minute hand and the hour hand of a clock when the time is $9:40,$ is?

• A. $40^{\circ}$
• B. $50^{\circ}$
• C. $70^{\circ}$
• D. $20^{\circ}$

Answer 1

In $60$ minutes the minute hand completes $360^o$ where as the hour hand travels only $360/12$ degrees. So,

$60M  \implies  \dfrac{360}{12} = 30^o  $

$9:40$ means $9\times 60 + 40 = 580M$

$580M \implies 30 \times 580/60 = 290^o.$

Now, in $40$ minutes the minute hand would have completed $360 \times 40 /60 = 240^o.$

So, angle of separation between minute and hour hands $ = 290-240 = 50^o.$

So, the correct answer is $(B).$

Comments

We can do simple logics too like hour hand covers 360 degree in  60 mins and then use some simple algebra can do this

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Lets do it in parts, clock is showing 9:40, so minute hand will be at 8 and lets assume that the hour hand it still at 9 exactly so they are 30degrees apart, then we know that it won’t be at 9 exactly, so as 40 minutes have passed that means $2/3^{rd}$ of an hour (60min) has passed. As the difference between two number is of 30 degrees and its 2/3rd’s is 20 degrees, add this to previous 30 degrees. Total we get 50 degrees.