Explanation

Convert the race distance from 1 km to meters: 1 km = 1000 m

Find the distance covered by X in the race: 48 m (given)

Find the distance covered by Y in the race: 42 m (given)

Since X beats Y, X covers the entire race distance (1000 m), while Y covers a shorter distance.

To find the distance by which X beats Y, subtract the distance covered by Y from the race distance: 1000 m - 42 m x (1000/48) = 1000 - 875 = 125 m

So, X beats Y by 125 meters.

Explanation

Track length = 1 km

Formula used:

Distance Speed x Time

Calculation:

"A" beats "B" by 50 m or 10 sec, means "B" covers 50 m in 10 sec

Speed of "B" = 50/10 = 5 m/s

Time to cover 1000 m = 1000/5 = 200 sec

"A" beats "B" by 10 sec means

"A" reach 10 sec early

Time taken by "A" to complete the race = 200 - 10 = 190 sec

∴ Time taken by "A" to complete the race is 190 sec.

Explanation

Volume of tank = 200 m x 150 m x 2 m = 60,000 m³

Volume of water flowing per second = (1.5 m x 1.25 m) x (20 km/h x (1000/3600)) = 208.33/9 m³/s

Time taken to fill the tank = 60,000 m³ / (208.33/9 m³/s) = 2600 seconds

Convert seconds to minutes = 2600 s / 60 = 43.33 minutes

Time taken to fill 2 meters = 43.33 x (2/3) = 96 minutes

Explanation

Length of the train = 240 m

Time taken to pass the pole = 24 seconds

Speed of the train = Distance / Time = 240 m / 24 s = 10 m/s

Total distance to be covered = Length of train + Length of platform = 240 m + 650 m = 890 m

Time taken to pass the platform = Total distance / Speed = 890 m / 10 m/s = 89 seconds

Explanation

Let's say the person's usual travel time to his office is x minutes.

Since he is walking at 5/6 of his usual speed, his new speed is 5/6 of his usual speed.

The time taken to cover the same distance at this new speed is 6/5 of his usual time (since speed and time are inversely proportional).

So, the new time taken = (6/5)x

Since he is 40 minutes late, the new time taken is 40 minutes more than his usual time:

(6/5)x = x + 40

Simplifying the equation:

(1/5)x = 40

x = 200 minutes

Converting x to hours and minutes:

x = 3 hours 20 minutes