If a man walks at the rate of 5 kmph, he misses a train by 7 minutes.

Question

If a man walks at the rate of 5 kmph, he misses a train by 7 minutes. However, if he walks at the rate of 6 kmph, he reaches the station 5 minutes before the departure of the train. Find the distance to the station.

A. 2 km
B. 3 km
C. 4 km
D. 5 km
E. 6 km

A. 2 km
B. 3 km
C. 4 km
D. 5 km
E. 6 km

cantaffordname · Accepted Answer

There's a 12 min difference in the times it takes him to walk the distance d at the 2 different speeds, so

d/5 – d/6 = 12/60 = 1/5 ............ multiply by 30

6d - 5d = 6

d = 6 km.

AnirudhaS · Answer

Let the distance to station be d kms

5 kms in 60 min
d kms in = 60/5*d = 12d min

6 kms in 60 min
d kms in = 60/10*d = 10d min

12d-10d = Difference in times = 12 
(the 12 comes from 7 minutes late and 5 minutes early, if time to reach is t min, then t+5-(t-7) = 12)
2d = 12
d=6 kms

Ans: E

jfranciscocuencag · Answer

I used the options:

Difference between the times must be 12 minutes.

Starting always with C.

C) 3km/5kmph = 36 min 1/2 = 30 min ---  Discard

D) 2km/5kmph = 24 min 1/3 = 20 min ---  Discard

E) 6km/5kmph = 72 min 6/6 = 60 min ---  Correct one

E

Emdad · Answer

We know,  D=\frac{Δt×S1×S2}{S1–S2}

So,  D=\frac{12×5×6}{60×1} 
=6 km
Answer is E

Posted from my mobile device

bv8562 · Answer

60 mins ------------- 5 km
1 min ---------------- 5/60 = 1/12 km/min

60 mins ------------- 6 kms
1 min --------------- 6/60 = 1/10 km/min

speed x time = distance

(t+7)/12 = d

(t-5)/10 = d

(t+7)/12 = (t-7)/10

t=65 mins

d = (t+7)/12 = 72/12 = 6 kms (E)

kopp74 · Answer

IMO E

d = t*s

below, x is the distance av. time needed to reach the station

(1)    d = 5 ( x + \frac{7}{60} )                           (First person walks at a speed of 5 kmph , and arrives 7 minutes late, which is 7/60 hours)

(2)    d = 6 ( x - \frac{5}{60} )                            (Second person walks at a speed of 6kmph , and arrives 5 minutes early , which is 5/60 hours)

(1)  =  (2)

5x + \frac{7}{12} = 6x - \frac{5}{10}

x = \frac{65}{60}

Replace  x=\frac{65}{60}  in  (1)  or  (2)  and get   d = 6 mins which is option E    
  This was my solution, hope you liked it.

riri3026 · Answer

Bunuel  
Can we solve it like this?

5*(t+7/60) = 6*(t-10/60)? 
As I use this every time for such questions but in this particular question I am getting 7 kms and not the required 6 kms

btsaami · Answer

You have taken 10 instead of 5.
5*(t+7/60)= 6*(t-10/60)

You can also find the time in minutes and convert to hour later if required.

bumpbot · Answer

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If a man walks at the rate of 5 kmph, he misses a train by 7 minutes.

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If a man walks at the rate of 5 kmph, he misses a train by 7 minutes.

Prep Toolkit

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