A train travels 360km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hour less for the same journey, then the actual speed of the train isa)36 km /hrb)48 km/hrc)45 km/hrd)40 km/hrCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Let the original speed of train be x

According to question -

360/x - 360/(x-5) = 1

By solving this the value of x will be 40 .

Hence , option d) is the correct answer.

Answer

Answer

Let the original speed of the train be x km/h.

Time taken to cover a distance of 360 km = 360/x hours.

New speed of the train = (x+5) km/h.

Time taken to cover a distance of 360 km at new speed = 360/x+5 hours.

Since, the train takes 1 hour less time,

∴ 360/x - 360/ x+5 = 1

⇒360 (x+5-x)/x(x+5) = 1

⇒360 (5) = x� + 5x

⇒1800 = x� + 5x

⇒x� + 5x - 1800 = 0

⇒x� + 45x - 40x - 1800 = 0

⇒x (x+45) - 40( x +45) = 0

⇒(x+45) (x-40) = 0

⇒x = (-45), 40

But since speed cannot be in negative.

∴ x = 40 km/hr.

Hence, the original speed of the train is 40 km/h.

Answer

Given:
- Distance traveled by the train = 360 km
- If the speed had been 5 km/hr more, it would have taken 1 hour less for the same journey.

To find:
The actual speed of the train.

Assumption:
Let the actual speed of the train be 'x' km/hr.

Calculating time taken at the actual speed:
- Distance = Speed × Time
- Time = Distance / Speed

At the actual speed 'x' km/hr, the time taken to travel 360 km is given by:
Time taken = 360 / x

Calculating time taken at the increased speed:
If the speed had been 5 km/hr more, the speed would be 'x + 5' km/hr.
At the increased speed 'x + 5' km/hr, the time taken to travel 360 km is given by:
Time taken = 360 / (x + 5)

Given condition:
The time taken at the increased speed is 1 hour less than the time taken at the actual speed.
So, we have the equation:
360 / (x + 5) = 360 / x - 1

Solving the equation:
To solve the equation, we can cross-multiply:
360x = (x + 5)(360 / x - 1)
360x = (360 + 1800 / x) - (x + 5)
360x = 360 + 1800 - x² - 5x
x² + 5x - 2160 = 0

This is a quadratic equation which can be solved using factorization or the quadratic formula. The factors of -2160 are -45 and 48.
(x - 45)(x + 48) = 0

This gives us two possible values for 'x':
x - 45 = 0 or x + 48 = 0
x = 45 or x = -48

Since speed cannot be negative, the actual speed of the train is 45 km/hr. Therefore, the correct answer is option C: 45 km/hr.

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