Question
A train started from station A and proceeded towards station B at a speed of 48 km/hr. Forty-five minutes later another train started from station B and proceeded towards station a at 50 km/hr. If the distance between the two stations is 232 km, at what distance from station A will the trains meet ?
Answer: Option B
Suppose the trains meet after x hrs
Then,
Distance covered by 1st train in x hrs + Distance covered by 2nd train in $$\left( {x - \frac{3}{4}} \right)$$ hrs = 232 km
$$\eqalign{
& \Rightarrow 48x + 50\left( {x - \frac{3}{4}} \right) = 232 \cr
& \Rightarrow 98x = 232 + \frac{{75}}{2} \cr
& \Rightarrow 98x = \frac{{539}}{2} \cr
& \Rightarrow x = \frac{{539}}{{196}}{\text{ hrs}} \cr} $$
Required distance = Distance travelled by 1st train in $$\left( {\frac{{539}}{{196}}} \right)$$ hrs
$$\eqalign{
& = \left( {48 \times \frac{{539}}{{196}}} \right){\text{km}} \cr
& = 132{\text{ km}} \cr} $$
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Suppose the trains meet after x hrs
Then,
Distance covered by 1st train in x hrs + Distance covered by 2nd train in $$\left( {x - \frac{3}{4}} \right)$$ hrs = 232 km
$$\eqalign{
& \Rightarrow 48x + 50\left( {x - \frac{3}{4}} \right) = 232 \cr
& \Rightarrow 98x = 232 + \frac{{75}}{2} \cr
& \Rightarrow 98x = \frac{{539}}{2} \cr
& \Rightarrow x = \frac{{539}}{{196}}{\text{ hrs}} \cr} $$
Required distance = Distance travelled by 1st train in $$\left( {\frac{{539}}{{196}}} \right)$$ hrs
$$\eqalign{
& = \left( {48 \times \frac{{539}}{{196}}} \right){\text{km}} \cr
& = 132{\text{ km}} \cr} $$
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