Question 4

A cyclist goes from a place P to Q; first at 4 km/h and later at 5 km/h in 1 hour 24 minutes altogether. If the distances covered in the first and second part of the journey are in the ratio 2 : 1, when did the cyclist change his speed after start?

Solution

Let total distance of the journey be $$3x$$ km..

Thus, the cyclist travelled $$2x$$ km at 4 km/hr and $$x$$ km at 5 km/hr

Using, time = distance/speed

=> $$\frac{2x}{4}+\frac{x}{5}=1+\frac{24}{60}$$

=> $$\frac{10x+4x}{20}=\frac{7}{5}$$

=> $$\frac{7x}{10}=\frac{7}{5}$$

=> $$x=2$$

Thus, total distance = 6 km, and the cyclist change his speed after travelling 4 km in = $$\frac{4}{4}=1$$ hour

=> Ans - (B)

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