GATE ECE 2020 | GA | Question: 7

Question

It is quarter past three in your watch. The angle between the hour hand and the minute hand is ________.

• A. $0^{\circ}$
• B. $7.5^{\circ}$
• C. $15^{\circ}$
• D. $22.5^{\circ}$

Comments

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Answer 1

$\text{Method I}:$
The angle between hour hand and minute hand of a clock at $H$ hours and $M$ minutes is given by $$\theta = 30H – \dfrac{11M}{2}$$So, at $03:15$ we get their difference as $30\times 3 - \frac{11(15)}{2}$
$\qquad= 90 – 82.5 = 7.5^{\circ}$

$\text{Method  II}:$

• $1 H = \frac{360}{12} = 30^{\circ}$
• $15 M = \frac{1}{4}H = \frac{30^{\circ}}{4} = 7.5^{\circ}$

Correct Option: B.

Comments

quarter past 3 means 2:45 or 3:15?

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@pavansan Quarter past 3 = 3:15 and 2:45 means Quarter to 3

Answer 2

The sentence “It is quarter past three in your watch.” is just a time expression. Here’s how to interpret it clearly 👇

Meaning

• Quarter = 15 minutes

• Past = after

• Three = 3 o’clock

So,

Quarter past three = 3:15

How to visualize it on a clock

• The minute hand is at 15 minutes (pointing at 3 on the clock)

• The hour hand is slightly ahead of 3, moving toward 4

General rule (very useful)

• Quarter past X → X:15

• Half past X → X:30

• Quarter to X → (X − 1):45

Example

• Quarter past five → 5:15

• Quarter to seven → 6:45

So in simple words:

“It is quarter past three” means the time is 3:15.

Answer 3

Prerequisite:

1hr mei angle by hr hand is 30deg

1 minute mei angle by hr hand 0.5 deg

15min mei angle by hr hand=15*0.5=7.5deg

solution:

3:15 pe angle by minute hand=90 degree(6 degree per minute so 15min*6)

3:15 pe angle by hr hand=90(1hr mei 30 so 3 hr mei 90) + 7.5(in 15min)

angle between =7.5