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Suman travells a distance of 120 km at a certain speed. If he increases his speed by 4 km/h, he takes 5 hrs less time to travel the same distance. Find his actual speed?
1. 8 km/h
2. 10 km/h
3. 6 km/h
4. 12 km/h

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Correct Answer - Option 1 : 8 km/h

Given:

Distance travelled = 120 km

Increase in speed = 4 km/h

Difference in time taken = 5 hrs

Formula used:

Time taken = Distance/speed

Calculation:

Let the initial speed = x km/h

∵ Initial time taken - New time taken = 5 hrs

⇒ 120/x - 120/(x + 4) = 5

⇒ 120x + 480 - 120x = 5x(x + 4)

⇒ 480 = 5x2 + 20x

⇒ x2 + 4x - 96 = 0

⇒ x2 + 12x - 8x - 96 = 0

⇒ x(x + 12) - 8(x + 12) = 0

⇒ (x - 8)(x + 12) = 0

∴ x - 8 = 0 

⇒ x = 8 km/h

x + 12 = 0

⇒ x = (-12) km/h Not possible

∴ Actual speed = 8 km/h

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