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One car runs from Jaipur to Shimla and the other from Shimla to Jaipur. They both start simultaneously and meet cross each other at a particular point on the route. The speeds of cars from Jaipur to Shimla and from Shimla to Jaipur are in the ratio 4 ∶ 3 respectively. After crossing each other the car from Jaipur to Shimla takes 5 hours to complete the leftover 250km of journey. The speed of the car from Shimla to Jaipur after crossing reduced by 10 km/h and it covered the leftover distance in 10 hours. What is the total distance between Jaipur and Shimla?

One car runs from Jaipur to Shimla and the other from Shimla to Jaipur. They both start simultaneously and meet cross each other at a particular point on the route. The speeds of cars from Jaipur to Shimla and from Shimla to Jaipur are in the ratio 4 ∶ 3 respectively. After crossing each other the car from Jaipur to Shimla takes 5 hours to complete the leftover 250km of journey. The speed of the car from Shimla to Jaipur after crossing reduced by 10 km/h and it covered the leftover distance in 10 hours. What is the total distance between Jaipur and Shimla? Correct Answer 525 km

Given:

The ratio of the speed of cars from Jaipur to Shimla and from Shimla to Jaipur = 4 ∶ 3

After crossing time taken by the car from Jaipur to Shimla to cover leftover 250 km of journey = 5 hours

The speed of the car from Shimla to Jaipur after crossing reduced by 10 km/h,

And it covered the leftover distance in 10 hours.

Formula:

Speed = distance/time

Calculation:

The ratio of the speed of cars from Jaipur to Shimla and from Shimla to Jaipur = 4 ∶ 3

Let the speed of cars from Jaipur to Shimla = 4x      ----(i)

And the speed of cars from Shimla to Jaipur = 3x      ----(ii)

After crossing time taken by the car from Jaipur to Shimla to cover leftover 250 km of journey = 5 hours

∵The car from Jaipur to Shimla cover 250 km of the journey in 5 hours

Then the speed of the car from Jaipur to Shimla

⇒ distance/time = 250/5 = 50 km/hr----(iii)

Now we compare equation (i) and (iii)

⇒ 4x = 50

⇒ x = 12.5 km/hr

Now put the value of x in equation (ii)

⇒ 3 × 12.5 = 37.5 km/hr

The speed of the car from Shimla to Jaipur after crossing reduced by 10 km/h,

Now the speed of the car from Shimla to Jaipur after crossing

⇒ 37.5 – 10 = 27.5 km/hr

The car from Shimla to Jaipur covered the leftover distance in 10 hours

Now, the distance that the car cover in 10 hours

⇒ 10 × 27.5 = 275 km

Now the total distance from Jaipur to Shimla

⇒ (The leftover distance for the car from Jaipur to Shimla + The leftover distance for the car from Shimla to Jaipur)

⇒ (250 + 275) = 525 km

∴The total distance between Jaipur and Shimla is 525 km.

Alternate method:

The car from Jaipur to Shimla

P

The car from  Shimla to Jaipur

Q

 

 

 

∵ The car P cover 250 km of journey in 5 hours

Then the speed of the car P = 250/5 = 50 km/hr

The ratio of speed of cars P and Q = 4 ∶ 3

The value of 4 = 50, then the value of 3 = (50/4) × 3 = 37.5 km/hr

The speed of car Q = 37.5 km/hr

The speed of car Q reduce by 10km/hr after crossing

Now the speed of car Q = 37.5 – 10 = 27.5 km/hr

The car Q covered the leftover distance in 10 hours

Now, the distance that the car cover in 10 hours

⇒ 10 × 27.5 = 275 km

Total distance = 250 + 275 = 525 km.

∴ The total distance between Jaipur and Shimla is 525 km.

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