Explanation

The hands of a clock coincide 22 times in a 24-hour day.

• The hour and minute hands coincide once every 65 minutes (60 minutes + 5 minutes).
• Since there are 24 hours in a day, the hands coincide 24 x (24/65) = 22 times in a 24-hour day.

Explanation

• Roni covers 100 meters in 45 seconds.
• Willy covers 100 meters in 36 seconds.

1. Roni's speed:

   Speed of Roni=100 m / 45 s​=20​/9 m/s

2. Distance Roni covers in 36 seconds:

   Distance=Speed×Time=20/9​×36=80 m

3. Since Willy finishes the race (100 m) when Roni has only covered 80 m, Willy beats Roni by:

   $$100-80=20\text{ m}$$

Explanation

Explanation

Total distance covered by both trains = 1160 + 1160 = 2320 meters

Time taken to cross each other = 20 seconds

Relative speed (combined speed of both trains) = Total distance / Time = 2320 / 20 = 116 meters/second

Since both trains have the same speed, the speed of each train = Relative speed / 2 = 116 / 2 = 58 meters/second

Convert meters/second to km/second: 58 / 1000 = 0.058 km/second (approximately)

Convert km/second to km/hour: 0.058 * 3600 = 208.8 km/hour

Explanation

Pipe A and pipe B can fill the tank in 3 hours and 5 hours, then total work = LCM of (3, 5) = 15 unit

Efficiency of pipe A = 15/3 = 5 unit and efficiency of pipe B = 15/5 = 3 unit

From 7 to 8 AM, pipe A alone done 5 unit, work remains (15 - 5) = 10 unit,

Now, pipe A and B together can do it in = 10/(5 + 3) = 10/8 hours = 10/8 × 60 = 75 min

 The required time is 8 AM + 75 min = 9 AM + 15 min = 9 : 15 AM

∴ The correct answer is 9 : 15 AM