CUET UG 2025 — General Test Arithmetic

Let the speed of the bus be $v$v km/hr and the length of the bus be $L$L meters.

When the bus passes a person moving in the same direction, the relative speed is the difference between their speeds.

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For the first person moving at 3 km/hr:

Relative speed $= (v - 3)$=(v−3) km/hr $= (v - 3) \times \dfrac{5}{18}$=(v−3)×185​ m/s

Time taken $= 10$=10 seconds

$$L = (v - 3) \times \dfrac{5}{18} \times 10$$L=(v−3)×185​×10

$$L = (v - 3) \times \dfrac{50}{18}$$L=(v−3)×1850​

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For the second person moving at 5 km/hr:

Relative speed $= (v - 5)$=(v−5) km/hr $= (v - 5) \times \dfrac{5}{18}$=(v−5)×185​ m/s

Time taken $= 11$=11 seconds

$$L = (v - 5) \times \dfrac{5}{18} \times 11$$L=(v−5)×185​×11

$$L = (v - 5) \times \dfrac{55}{18}$$L=(v−5)×1855​

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Since the length of the bus is the same in both cases:

$$(v - 3) \times \dfrac{50}{18} = (v - 5) \times \dfrac{55}{18}$$(v−3)×1850​=(v−5)×1855​

$$(v - 3) \times 50 = (v - 5) \times 55$$(v−3)×50=(v−5)×55

$$50v - 150 = 55v - 275$$50v−150=55v−275

$$275 - 150 = 55v - 50v$$275−150=55v−50v

$$125 = 5v$$125=5v

$v = 25$v=25 km/hr

Therefore, the speed of the bus is 25 km/hr.

The answer is option 3.