A and B travel same distance at speed of 9 km/hr and 10 km/hr respectively. If A takes 36 min more than B, distance travelled by each is :

Let tistance between A and B be $$x$$ km, then
$$\eqalign{ & \frac{x}{9} - \frac{x}{{10}} = \frac{{36}}{{60}} \cr & \Rightarrow \frac{x}{{90}} = \frac{3}{5} \cr & \Rightarrow x = \frac{3}{5} \times 90 \cr & \Rightarrow x = 54\,{\text{km}} \cr & {\text{Hence option B is correct}} \cr} $$

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$$\eqalign{ & \text{Alternate Solution:} \cr & {\text{Here,}}\,{s_1} = 9,\,{t_1} = x \cr & {s_2} = 10,\,{t_2} = x - \frac{{36}}{{60}} \cr & {s_1}{t_1} = {s_2}{t_2} \cr & \Rightarrow 9 \times x = 10\times\left( {x - \frac{{36}}{{60}}} \right) \cr & \Rightarrow 9 9x = 10x - 6 \cr & \Rightarrow 9 x = 6 \cr & \therefore {\text{ Distance }}\,{\text{travelled}} \cr & = s_1 \times t_1 \cr & = 9 \times 6 \cr & = 54\,\,{\text{km}} \cr} $$