2026 · Q66
The smaller angle made by the hour and the minute hands is noted when it was 1:30 PM. In which of the following intervals of time will the smaller angle between these hands again be the same?
general-mental-abilityquantitative-aptitude
- A1:44 PM and 1:45 PM
- B1:45 PM and 1:46 PM
- C1:46 PM and 1:47 PM
- D1:47 PM and 1:48 PM
Explanation
At 1:30 the hour hand is at 45° and the minute hand at 180°, so the smaller angle is 135°. The hands separate at 5.5° per minute; the angle grows to 180° at about 1:38.2 and then the smaller angle shrinks. It equals 135° again when the separation reaches 225°, i.e., at t = 255/5.5 ≈ 46.4 minutes past 1:00 — about 1:46.4, which falls in the interval 1:46 PM to 1:47 PM. Hence option C is correct.