From point P, X walks at a speed of 12 Km/hr and 6 hours after his start, Y also starts walking from same point P on his cycle after him at the speed of 16 km/hr. How far from the starting point P will Y catch X?

a) 224 km
b) 288 km
c) 256 km
d) 324 km

Ans : b) 288 km

SSC Constable GD Exam paper (21 Feb 2024)

Solution

To find out how far from point P Y will catch X, we need to calculate the distance each has traveled when Y catches up to X.

Distance traveled by X in 6 hours before Y starts: $\text{Distance} = \text{Speed} \times \text{Time} = 12 , \text{km/hr} \times 6 , \text{hr} = 72 , \text{km}$

Relative speed of Y catching up to X: $\text{Relative Speed} = 16 , \text{km/hr} - 12 , \text{km/hr} = 4 , \text{km/hr}$

Time taken by Y to catch up to X: $\text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{72 , \text{km}}{4 , \text{km/hr}} = 18 , \text{hours}$

Distance traveled by Y in 18 hours: $\text{Distance} = \text{Speed} \times \text{Time} = 16 , \text{km/hr} \times 18 , \text{hr} = 288 , \text{km}$

So, Y will catch X 288 km from the starting point P.

From point P, X walks at a speed of 12 Km/hr and 6 hours after his start, Y also starts walking from same point P on his cycle after him at the speed of 16 km/hr. How far from the starting point P will Y catch X?

Solution

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