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Question:

Riya runs 3/2 times as fast as Prerna. In a race, if Riya gives a lead of 100 m to Prerna, find the distance Riya has to run before both of them meet.

Explanation:

Ratio of speeds of Riya and Prerna = 3 : 2

Let Prerna run P meters before Riya catches up with her. 
⇒ Distance travelled by Riya = P + 100

∴ $\frac{\mathrm{Distance} \mathrm{covered} \mathrm{by} \mathrm{Riya}}{\mathrm{Distance} \mathrm{covered} \mathrm{by} \mathrm{Prerna}}$ = $\frac{\mathrm{P}+100}{\mathrm{P}}$ = $\frac{3}{2}$

⇒ 2P + 200 = 3P

⇒ P = 200

∴ Distance travelled by Riya = P + 100 = 300 meters.

Hence, option (b).