Ram singh goes to his office in the city every day from his suburban house. His driverMangaram drops him at the railway station in the morning and picks him up in the evening.Every evening Ram singh reaches the station at 5 o'clock. Mangaram also reaches at thesame time. One day Ram singh started early from his office and came to the station at 4o'clock. Not wanting to wait for the car he starts walking home. Mangaram starts at normaltime, picks him up on the way and takes him back house, half an hour early. How much timedid Ram singh walked?

Madhusmita_behera
Profile Answers by Madhusmita_behera Questions by Madhusmita_behera
Sep 21st, 2006
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ashokkumarnimmala
Profile Answers by ashokkumarnimmala

Jul 27th, 2008

They reached thirty minutes earlier than what they normally do so the car and ramsingh have met at 4.45
since these thirty minutes (going to station from that point and coming back to that point) are saved so ram singh walked for 45 minutes hence the answer is 45 minutes

rahuliit2003
Profile Answers by rahuliit2003

Feb 23rd, 2009

Assume their speeds Vrs & Vm and the time for which Ram Singh walks be t, total distance be S

Equation 1) First condition, for the two men to meet, they have to meet at the same time in the reference frame.

    for them to meet,

      4 + t = 5 - S/Vm + {S - (Vrs x t)/Vm)}

[ L.H.S is time of Ram Singh, R.H.S being time taken for Mangaram. 4 and 5 are times in 4p.m. and 5 p.m.]

Equation 2) When they go by walking for some distance and driving the other diatcne, they reach half an hour earlier than everyday.

   5 + S/Vm - 0.5 = 4 + t + {S - (Vrs x t)}/Vm

[L.H.S being everyday's time (5 + S/Vm) minus the half an hour (0.5)
R.H.S being 4'o clock(4) + time ram singh walked(t) + time taken to cover the remaining distance by car( S- Vrsxt)/Vm

solving the equations we get Vrs/Vm = 1/3 and t = 0.75