Question

Q 10
Ram beats Laxman by 20 m in a 100 m race. Bharat beats Laxman by 25 m in a 100
m race. If they run at the same speed in a 400 m race, by how many meters will
Bharat beat Ram?​

Answer 1

In hundred minutes Bharat beat ram

Answer 2

Answer:

Bharat beats Ram by 25 metres in the 400 metres race

Step-by-step explanation:

It is given Ram beats Laxman by 20 metres in 100 metres Race

So by the time Ram finishes 100 metres, Laxman will have finished 80 metres (100 - 20 = 80)

=> By the time Ram finishes (100/20) metres, Laxman will have finished (80/20) metres  ----> Dividing the 2 numbers by 20 (20 is the HCF of 100 and 80)

=> By the time Ram finishes 5 metres, Laxman will have finished                    4 metres ---> Statement 1

Now Bharat beats Laxman by 25 m in 100 metres race

So by the time Bharat finishes 100 metres, Laxman will have finished 75 metres (100 - 25)

By the time Bharat finishes (100/25) metres, Laxman will have finished (75/25) metres ----> Dividing the 2 numbers by 25 (25 is the HCF of 100 and 75)

=> By the time Bharat finishes 4 metres, Laxman will have finished

3 metres ---> Statement 2

Now, we must find by how many meters will  Bharat beat Ram in a 400 metres race

That is, we must find the distance Ram covered when Bharat finished 400 metres

To this, let's first find out the distance Laxman covered when Bharat finished the 400 metres

We know that  By the time Bharat finishes 4 metres, Laxman will have finished 3 metres (from Statement 2)

=> By the time Bharat finishes (4 * 100) metres, Laxman will have finished   (3 * 100) metres -----> Multiplying both numbers by 100 to get the distance Laxman covered when Bharat finished the 400 metres  

=> By the time Bharat finishes 400 metres, Laxman will have finished 300 metres ------> Statement 3

Now, let's find out the distance covered by Ram when Laxman had covered 300 metres

We know that  By the time Ram finishes 5 metres, Laxman will have finished 4 metres (From statement 1)

=>  By the time Laxman finishes 4 metres, Ram will have finished by 5 metres

=> By the time Laxman finishes (4*75)  metres, Ram will have finished by (5*75) metres   ----> Multiplying by 75 to get distance covered by Ram when Laxman finishes 300 metres

By the time Laxman finishes 300 metres, Ram will have finished

375 metres  ----> Statement 4

So by the time Laxman finishes 300 metres, Bharat would have finished 400 metres, and Ram would have finished 375 metres (From statements 3 and 4)

So, by the time Bharat finishes 400 metres, Ram will have finished 375 metres

So, Bharat beats Ram by 25 metres in the 400 metres race