Question

Given below are two statements: Assertion (A): The angle between the two arms of a watch when the time is \(3.10\) pm will be \(35^\circ\). Reason (R): When the hour arm of the watch is ahead of the minute arm, then angle between the two arms at the time \(t\) hour and \(x\) minute is \(\left[30\left(t-\frac{x}{5}\right)+\frac{x{2}\right]^\circ\).}

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

For clock angle problems, substitute hour and minute carefully in the angle formula.

Answer 1

The Correct Option is A

At \(3:10\), the hour hand is between \(3\) and \(4\). The minute hand is at \(10\) minutes. The given formula is: \[ \left[30\left(t-\frac{x}{5}\right)+\frac{x}{2}\right]^\circ. \] Here: \[ t=3,\qquad x=10. \] Substitute: \[ 30\left(3-\frac{10}{5}\right)+\frac{10}{2}. \] \[ =30(3-2)+5. \] \[ =30(1)+5. \] \[ =35^\circ. \] So the assertion that the angle is \(35^\circ\) is correct. The reason gives the correct formula and also explains the calculation. Therefore, both Assertion and Reason are correct, and Reason correctly explains Assertion. Hence, the correct answer is option (A).