CAT 2017

Slot 2

QA

Question & Solution

1. Concept Used

• Topic: Time, Speed and Distance — Relative Motion between two objects moving toward each other
• Formula: $$\text{Distance} = \text{Speed} \times \text{Time}, \quad \text{Speed of Car} = 2 \times \text{Speed of Motorbike}$$

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2. Calculation

Let the speed of the motorbike be $$v$$ km/h. Then the speed of the car is $$2v$$ km/h.

Time traveled by the motorbike: It leaves at 1:00 pm and they meet at 3:40 pm, so the motorbike travels for $$2$$ hours $$40$$ minutes $$= \frac{8}{3}$$ hours.

The motorbike covers 168 km in this time, so: $$v = \frac{168}{\frac{8}{3}} = \frac{168 \times 3}{8} = \frac{504}{8} = 63 \text{ km/h}$$

Time traveled by the car: It leaves at 2:00 pm and they meet at 3:40 pm, so the car travels for $$1$$ hour $$40$$ minutes $$= \frac{5}{3}$$ hours.

The speed of the car is $$2v = 2 \times 63 = 126$$ km/h.

Distance covered by the car: $$d_{\text{car}} = 126 \times \frac{5}{3} = 42 \times 5 = 210 \text{ km}$$

Verification of speed ratio: We can verify: $$\frac{d_{\text{car}}}{\text{time of car}} = \frac{210}{\frac{5}{3}} = 126$$ and $$\frac{168}{\frac{8}{3}} = 63$$. Indeed $$126 = 2 \times 63$$ ✅

Total distance between A and B: $$AB = d_{\text{motorbike}} + d_{\text{car}} = 168 + 210 = 378 \text{ km}$$

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3. Solution

Answer = Option B ✅

The final calculated distance between A and B is 378 km.