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A train covers a distance of 480 km at a uniform speed. If the speed had been 8km/hr less than it would have taken 3 hours more to cover the same distance. Find the usual speed of the train.

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38 km/hr

39 km/hr

41 km/hr

40 km/hr

answer is C.

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Detailed Solution

Given that, train covers a distance of 480 km at a uniform speed.
Let’s assume the usual speed of the train is

s

km/hr and time taken for the usual speed be

t

then,
Time

= \frac{480}{s}

\{Time = \frac{Distance}{speed}\}

Time required for the train when speed was reduced by 8 km/hr,
Time

= \frac{480}{s - 8}

\{Time = \frac{Distance}{speed}\}

According to question, if the speed had been 8km/hr less than it would have taken 3 hours more to cover the same distance then,

⟹ \frac{480}{s - 8} = \frac{480}{s} + 3

⟹ \frac{480}{s - 8} - \frac{480}{s} = 3

⟹ \frac{480 s - 480 (s - 8)}{s (s - 8)} = 3

⟹ \frac{480 s - 480 s + 3840}{s^{2} - 8 s} = 3

⟹ 3 (s^{2} - 8 s) = 3840

⟹ 3 s^{2} - 24 s - 3840 = 0

⟹ s^{2} - 8 s - 1280 = 0

⟹ s^{2} - 40 s + 32 s - 1280 = 0

⟹ s (s - 40) + 32 (s - 40) = 0

⟹ (s + 32) (s - 40) = 0

⟹ s + 32 = 0 or s - 40 = 0

∴ s = - 32 or s = 40

∴

The usual speed of the train is 40 km/hr.
Hence, option (3) is correct.

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