Question

A train M leaves City A at 5 am and reaches City B at 9am . Another train N leaves City B at 7am and reaches City A at 1030am. At what time do the 2 trains cross one another? 

A.    1 hr 23 min


B.    1 hr 15 min


C.    1 hr 8 min


D.    56 min

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Answer 1

Answer : D.

Let the distance between the cities be x

They meet after y hr after 7am

M covers x in 4hr

N covers x in 3 ½ i.e 7/2 hr

speed of M =x/4

speed of N = 2x/7

Distance covered by M in y+2 hr + Distance covered by N in

y hr is x

x/4 (y+2) +2x/7(y)=x

y=14/15hr or 56 min

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Answer 2

Given:

• Let the distance between A and B be x Km
• Let the two trains meet after y hours after 7 am

To Find:

• Time at which the two trains cross each other.

Solution:

• By the given data, we can say that train M covers x Km in 4 hours.
• Train N covers x Km in (7/2) hours.
• Speed of train M = $\frac{x}{4} Km/hr$
• Speed of train N = $\frac{2x}{7}Km/hr$
• The value of x = (distance of M covered in (y+2) hours )+ (distance covered in y hours).
• x = $\frac{x}{4}(y+2)+\frac{2x}{7}y$ = $\frac{y+2}{4} +\frac{2y}{7} = 1$
• $\frac{(y+2)7+8y}{28} = 1$
• $\frac{7y+14+8y}{28} = 1$
• $\frac{15y+14}{28} = 1$
• $15y+14 = 28$
• $15y = 28-14$
• $15y = 14$
• $y = \frac{14}{15}$ hours = 56 mins.

The answer is 56 mins. (option D)

As the two trains will meet after 7 am, the exact time where they will cross each other is 7:56 am.