Question
Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Answer: Option B
$$\eqalign{
& {\text{Suppose}}\,{\text{they}}\,{\text{meet}}\,x\,{\text{hours}}\,{\text{after}}\,{\text{7}}\,{\text{a}}{\text{.m}}. \cr
& {\text{Distance}}\,{\text{covered}}\,{\text{by}}\,{\text{A}}\, \cr
& {\text{in}}\,x\,{\text{hours = 20x}}\,{\text{km}}{\text{.}} \cr
& {\text{Distance}}\,{\text{covered}}\,{\text{by}}\,{\text{B}} \cr
& \,{\text{in}}\,\left( {x - 1} \right)\,{\text{hours}} = 25\left( {x - 1} \right)\,km \cr
& \therefore 20x + 25\left( {x - 1} \right) = 110 \cr
& \Rightarrow 45x = 135 \cr
& \Rightarrow x = 3 \cr
& {\text{So,}}\,{\text{they}}\,{\text{meet}}\,{\text{at}}\,{\text{10}}\,{\text{a}}{\text{.m}}{\text{.}}\, \cr} $$
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$$\eqalign{
& {\text{Suppose}}\,{\text{they}}\,{\text{meet}}\,x\,{\text{hours}}\,{\text{after}}\,{\text{7}}\,{\text{a}}{\text{.m}}. \cr
& {\text{Distance}}\,{\text{covered}}\,{\text{by}}\,{\text{A}}\, \cr
& {\text{in}}\,x\,{\text{hours = 20x}}\,{\text{km}}{\text{.}} \cr
& {\text{Distance}}\,{\text{covered}}\,{\text{by}}\,{\text{B}} \cr
& \,{\text{in}}\,\left( {x - 1} \right)\,{\text{hours}} = 25\left( {x - 1} \right)\,km \cr
& \therefore 20x + 25\left( {x - 1} \right) = 110 \cr
& \Rightarrow 45x = 135 \cr
& \Rightarrow x = 3 \cr
& {\text{So,}}\,{\text{they}}\,{\text{meet}}\,{\text{at}}\,{\text{10}}\,{\text{a}}{\text{.m}}{\text{.}}\, \cr} $$
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