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Mohan plans to travel to his village which is 300 km. He plans to travel 20% of the journey first by car and remaining by train. The speed of the train and car is 80 km/hr and 60 km/hr respectively. Mohan travelled first 20% by car but as he reached the railway station he missed the train and decides to travel all the distance by car so he increases the speed and reaches on time. What percent should be the increase in speed of the car so as to reach on time?

Mohan plans to travel to his village which is 300 km. He plans to travel 20% of the journey first by car and remaining by train. The speed of the train and car is 80 km/hr and 60 km/hr respectively. Mohan travelled first 20% by car but as he reached the railway station he missed the train and decides to travel all the distance by car so he increases the speed and reaches on time. What percent should be the increase in speed of the car so as to reach on time? Correct Answer 33.33%

Given:

Distance between his current position to village is 300 km

Speed of the train = 80 km/hr

Formula Used:

Speed = Distance/time

Calculation:

Let Increased speed of car be y km/hr

Speed of the train = 80 km/hr

In the first case,

Distance travelled by car =  20% of 300 km = 60 km

Distance travelled by train =  80% of 300 km = 240 km

Time taken for the journey

t1 = = 60/60 + 240/80     ---(1)

In the second case,

Distance travelled by car = 300 km

Time taken for the journey

t2 = 60/60 + 240/y       ----(2)

As the time taken is equal in both cases, then

From equation (1) & (2)

60/60 + 240/80 = 60/60 + 240/y

⇒ 3 = 240/y 

⇒ y = 80 km/hr 

∴ Percentage Increase in the speed = (80 - 60)/60 × 100 = 33.33%

Confusion PointsIt is given that when he misses the train he decides to cover the whole journey with his car. So, it is clearly depicted that he must be travelling initially with the speed given in the question initially.

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