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

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

Explanation

In 1/h hour the student solves q questions

In 1/h*h hours the student will solve q*h questions

That is in 1 hour the student will solve q*h questions.

So in q hours, the student will solve q*q*h questions

So your answer is:-  q²h questions

Sh31-8-2023

Explanation

Distance = 500 m = 0.5 km (since 1 km = 1000 m)

Time = 5 minutes = 5/60 = 1/12 hours (since 1 hour = 60 minutes)

Speed = Distance / Time = 0.5 km / (1/12) hours = 0.5 km × 12/1 = 6 km/h

So, the correct answer is: 6

Explanation

This problem involves a proportional relationship between machines, work, and time.

We are told that:

• 5 machines do 5 works in 5 minutes.

The rate at which each machine works is:

Rate of 1 machine= 5 works/ 5machines×5minutes= 1 works / 5minutes​

So, 1 machine can complete 1 work in 5 minutes.

Explanation

First, find the speed of the train past the telegraph post:

Speed = Distance / Time = (Length of train) / 8 seconds

Since the length of the train is not given, let's call it "x". Then, Speed = x / 8

Now, find the speed of the train past the bridge:

Speed = Distance / Time = (Length of train + Length of bridge) / 20 seconds

= (x + 264) / 20

Since the speed of the train is the same in both cases, set up an equation:

x / 8 = (x + 264) / 20

Cross-multiply and solve for x:

20x = 8x + 2112

12x = 2112

x = 176

So, the length of the train is 176 meters.

Now, find the speed of the train:

Speed = x / 8 = 176 / 8 = 22 meters/second

Convert the speed to km/hr:

Speed = 22 m/s x (3600 s/h) / (1000 m/km) = 79.2 km/hr

The correct answer is:

79.2 km/hr

Explanation

To find the new time required to complete the task, divide the original time by the number of workers:

25 hours ÷ 5 workers = 5 hours

So, if 4 people with the same efficiency join you, it will take 5 hours to clean the garden.

Explanation

Let's break down the movements step by step:

East 10 meters:

You are now 10 meters east of your house from the starting point.

North 15 meters:

Now you're 10 meters east and 15 meters north of your house.

West 12 meters:

Moving west by 12 meters puts you 2 meters west of your house (because 12 - 10 = 2).

South 15 meters:

Moving south 15 meters brings you back to your house's north-south position (because 15 meters north - 15 meters south = 0).

So now you're 2 meters west and 0 meters north-south from your house.

The distance from your house is simply 2 meters.