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Distance between ram and his office is 600Km. One day he started at normal speed and cover 2/3rd of the distance And as forgot to take the key of office he returned at the same moment with 3/2 of the original speed. And then again gone to office with double speed and noticed that he had reached 20 minutes earlier. What will be the original speed of ram?
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Distance between ram and his office is 600Km. One day he started at no...
Given:
Distance between Ram's house and office = 600 km
Ram covers 2/3rd of the distance at his normal speed.
While returning, Ram covers the same distance with 3/2 times his normal speed.
When he goes to the office again, he doubles his speed and reaches 20 minutes earlier.

To find:
The original speed of Ram.

Assumption:
Let's assume Ram's normal speed is x km/hr.

Explanation:

Distance covered in the first trip:
Ram covers 2/3rd of the distance at his normal speed.
Distance covered in the first trip = (2/3) * 600 = 400 km

Time taken in the first trip:
Time = Distance / Speed
Time taken in the first trip = 400 / x = 400x / x = 400 hours

Distance covered in the return trip:
Ram covers the same distance with 3/2 times his normal speed.
Distance covered in the return trip = 400 km

Time taken in the return trip:
Time = Distance / Speed
Time taken in the return trip = 400 / (3/2)x = 400 * (2/3x) = 800 / 3x hours

Distance covered in the second trip:
Ram covers the remaining 1/3rd of the distance with double the speed.
Distance covered in the second trip = (1/3) * 600 = 200 km

Time taken in the second trip:
Time = Distance / Speed
Time taken in the second trip = 200 / (2x) = 100 / x hours

Total time taken:
Total time taken = Time taken in the first trip + Time taken in the return trip + Time taken in the second trip
Total time taken = 400 hours + 800/3x hours + 100/x hours

Given that Ram reached 20 minutes earlier:
Total time taken - 20 minutes = Total time taken
400 hours + 800/3x hours + 100/x hours - 20/60 hours = 400 hours + 800/3x hours + 100/x hours

Simplifying the equation:
20/60 hours = 800/3x hours + 100/x hours
1/3 hours = 800/3x hours + 100/x hours

Multiplying through by 3x:
x = 800 + 300

Simplifying:
x = 1100

Therefore, the original speed of Ram is 1100 km/hr.
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