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CUET General Test 2025 PYQs20 May Shift 2. Free, no login required.

Arithmetic

past year questions, CUET General Test 2025 20 May Shift 2

Time, Speed & Distance

past year questions, Arithmetic, CUET General Test 2025 20 May Shift 2

Medium

A bus passes two persons moving in the direction of the moving bus at a speed of 3 km/hr and 5 km/hr, respectively. The bus passes the first person in 10 s and the second person in 11 s. Find the speed of the bus.

Solution

✅ Correct Option: 3

Let the speed of the bus be vv km/hr and the length of the bus be LL meters.

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

For the first person moving at 3 km/hr:

Relative speed =(v−3)= (v - 3) km/hr =(v−3)×518= (v - 3) \times \dfrac{5}{18} m/s

Time taken =10= 10 seconds

L=(v−3)×518×10L = (v - 3) \times \dfrac{5}{18} \times 10

L=(v−3)×5018L = (v - 3) \times \dfrac{50}{18}

For the second person moving at 5 km/hr:

Relative speed =(v−5)= (v - 5) km/hr =(v−5)×518= (v - 5) \times \dfrac{5}{18} m/s

Time taken =11= 11 seconds

L=(v−5)×518×11L = (v - 5) \times \dfrac{5}{18} \times 11

L=(v−5)×5518L = (v - 5) \times \dfrac{55}{18}

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

(v−3)×5018=(v−5)×5518(v - 3) \times \dfrac{50}{18} = (v - 5) \times \dfrac{55}{18}

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

50v−150=55v−27550v - 150 = 55v - 275

275−150=55v−50v275 - 150 = 55v - 50v

125=5v125 = 5v

v=25v = 25 km/hr

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

The answer is option 3.

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