Question
Two trains are coming from opposite directions with speed of 75 km/hr and 100 km/hr on to parallel tracks. At some moment the distance between them is 100km. After T hours, distance between them is again 100 km. T is equal to?
Answer: Option B
$$\eqalign{
& {\text{Relative speed}} \cr
& {\text{ = (75 + 100)km/hr}} \cr
& {\text{ = 175 km/hr}} \cr
& {\text{Time taken to cover 175 km}} \cr
& {\text{at relative speed = 1 hr}} \cr
& \therefore {\text{T = Time taken to cover 200 km}} \cr
& {\text{ = }}\left( {\frac{1}{{175}} \times 200} \right)\, \text{hr} \cr
& = \frac{8}{7}\, \text{hr} \cr
& = 1\frac{1}{7}\, \text{hr} \cr} $$
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$$\eqalign{
& {\text{Relative speed}} \cr
& {\text{ = (75 + 100)km/hr}} \cr
& {\text{ = 175 km/hr}} \cr
& {\text{Time taken to cover 175 km}} \cr
& {\text{at relative speed = 1 hr}} \cr
& \therefore {\text{T = Time taken to cover 200 km}} \cr
& {\text{ = }}\left( {\frac{1}{{175}} \times 200} \right)\, \text{hr} \cr
& = \frac{8}{7}\, \text{hr} \cr
& = 1\frac{1}{7}\, \text{hr} \cr} $$
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