In a 400 m race, A gives B a start of 5 seconds and beats him by 15 m. In another race of 400 m, A beats B by 71/7 seconds. Their respective speed are -

Answer: Option C

Suppose A covers 400 m in t seconds
Then, B covers 385 m in (t + 5) seconds
$$\begin{array}{rl}& \therefore \text{ B covers 400 m in}\\ & =\left\{\frac{\left(t+5\right)}{385}\times 400\right\}\text{ sec}\\ & =\frac{80\left(t+5\right)}{77}\text{ sec}\\ & \text{Also, B covers 400 m in}\\ & =\left(t+7\frac{1}{7}\right)\text{ sec}\\ & =\frac{\left(7t+50\right)}{7}\text{ sec}\\ & \therefore \frac{80\left(t+5\right)}{77}=\frac{7t+50}{7}\\ & \Rightarrow 80\left(t+5\right)=11\left(7t+50\right)\\ & \Rightarrow \left(80t-77t\right)=\left(550-400\right)\\ & \Rightarrow 3t=150\\ & \Rightarrow t=50\\ & \therefore \text{ A’s speed}\\ & =\frac{400}{50}m/\sec \\ & =8m/\sec \\ & \therefore \text{B’s speed}\\ & =\frac{385}{55}m/\sec \\ & =7m/\sec \end{array}$$