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Question
Choose the most appropriate option.
A train ‘X’ leaves station ‘A’ at 3 p.m and reaches station ‘B’ at 4.30 p. m., while another train ‘Y’ leaves station ‘B’ at 3.00 p.m and reaches station ‘A’ at 4.00 p.m. These two trains cross each other at:
Options
3.36 p.m.
3.30 p.m.
3.20 p.m.
3.40 p.m.
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Solution
3.36 p.m.
Explanation:
Let the distance between station A and station B = d km
Train x covers distance d km in`1 1/2=3/2` hr
∴ Speed of train x`="d"/((3/2))=(2"d")/3` Km/hr
Train y covers distance d km in 1 hr
∴ Speed of the train y`="d"/1` =d km /hr
Let the trains meet x hours after 3 pm
Distance travelled by train x in x hours
`= "x"xx(2"d")/3`km
Distance travelled by train y in x hours
= x × d km
Sum of these distance must be the total distance between station A and B
`"x"xx(2"d")/2+"x"xx"d"="d"`
`"x"+(2"x")/3=1`
`(5"x")/3=1`
`3/5`hr = 36 minutes
So, train eill cross each other at 3.36 p.m.
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