The angle between hour hand and the minute hand at 3:40 pm is ?

Appeared in: PGIMER Chandigarh NO - 2015

Explanation

The correct angle at 3:40 is 130 degrees.
The most direct way to solve this is using the formula: Angle = |30H - 5.5M|, where H is the hour and M is the minute.
Substituting the values H=3 and M=40 gives: |(30 x 3) - (5.5 x 40)| = |90 - 220| = |-130| = 130 degrees.
Alternatively, one can calculate the position of each hand from the 12 o'clock mark. The minute hand is at 240 degrees (40 x 6), and the hour hand is at 110 degrees ((3 x 30) + (40 x 0.5)). The difference is 130 degrees.

Option A: This is an incorrect calculation. It might result from rounding values or using an incorrect formula.
Option B: This is a calculation error. It is close to the correct answer but not precise.
Option D: This is an incorrect calculation. It might arise from miscalculating the hour hand's movement. For example, assuming the hour hand is exactly on the 3 (90 degrees) and the minute hand is on the 8 (240 degrees), the difference is 150 degrees. This ignores the fact that the hour hand has moved past the 3.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the angle between the hands of a clock at a specific time as background academic context rather than a clinical decision trigger.
This type of question assesses logical reasoning and mathematical aptitude, which are foundational skills for nurses.
Nurses use similar problem-solving skills for critical tasks such as calculating medication dosages, titrating IV drips, and interpreting patient data charts, where precision is vital for patient safety.
What if the time was 10:10? The angle would be |(30 x 10) - (5.5 x 10)| = |300 - 55| = 245 degrees. Since this is a reflex angle (greater than 180), the smaller angle is 360 - 245 = 115 degrees. This shows the importance of considering both the direct and reflex angles.

How to Approach the Question

First, identify the hour (H) and minute (M) values from the given time. For 3:40, H=3 and M=40.
Recall the standard formula for finding the angle between the hands of a clock: Angle = |30H - 5.5M|.
Substitute the values of H and M into the formula: Angle = |(30 x 3) - (5.5 x 40)|.
Perform the multiplication and subtraction inside the absolute value bars: Angle = |90 - 220| = |-130|.
The absolute value of -130 is 130. Therefore, the angle is 130 degrees.
Compare your result with the given options to find the correct answer.

Concept Tested & Keywords

Concept Tested: Calculating the angle between the hands of a clock at a specific time.
Stem keywords: angle, hour hand, minute hand, 3:40 pm
Lead-in keywords: BEST, MOST RELEVANT CLUE
Negative lead-in flag: false

QmFFd7ZEtD8njcD2wAikMk

Practise the full PGIMER Chandigarh NO - 2015

Attempt every question from this paper in a timed mock, then review the full solution for each one.