PT Usha and Shelly John decide to run a marathon between Ramnagar and Jamnagar. Both
start from Ramnagar at 1 pm. On the way are two towns Ramgarh and Rampur, separated
by a distance of 15 km. PT Usha reaches Ramgarh in 90 minutes running at a constant
speed of 40 kmph. She takes additional 30 minutes to reach Rampur. Between Rampur and
Jamnagar she maintains an average speed of V kmph (where V is a whole number),Shelly
John being a professional marathon runner, maintains a constant speed of 18 kmph. They
both reach Jamnagar together after ‘n’ hours, ‘n’ being a whole number. What could be total
time taken by PT Usha?
a) 5 hours b) 15 hours c) 41 hours d) All of the above

• answer 5 hours
  
  ramnagar-------60km------ramgrah-------15km-----rampur----(n-2)vkm----jamnagar
  
  total distance covered by shelly =18n
  total distance covered by usha =60+15+(n-2)v=75+nv-2v
  
  18n =75+nv-2v
  
  18n-nv= 75-2v
  
  n(18-v) =75-2v
  
  n =75-2v/18-v
  
  as n being a natural number the only satisfying above equation is when v =5
  
  then n=65/13 =5
• 8 years agoHelpfull: Yes(37) No(9)
• PT USHA-
  Ramnagar to ramgarh-
  speed=40 kmph
  time taken= 90 mins
  distance covered=60 km.
  ramgarh to rampur
  dist= 15 km
  time taken =30 mins
  speed= 30 kmph
  rampur to jamnagar-
  speed is 'V'
  Noe,
  shelly maintains speed 18kmph throughout the journey ..distance from ramnagar to rampur =60+15=75 kms.
  time taken by shelly to cover 75 km= 75/18= 4 hours 10 mins.
  Now they reach jamnagar together so the next whole number is 5 so time taken by PT Usha is also 5 hours.
  Now distance from rampur to jamnagar.
  Using PT Usha stats: (N-2)*V.
  Using Shelly Stats: 18*N - 75.
  
  Therefore (N-2)*V = 3*(6*N -2 5) is the equation and V and n are whole number.
  
  Considering a)N= 5 : V=5 from the eqn
  B) N=15 : V=15.
  C) N=41: V=17.
  
  Since V is less than 18Kmph in all situation d) All of the above is the ans
• 8 years agoHelpfull: Yes(12) No(1)
• In (n-2) where does 2 comes from@deepak
• 8 years agoHelpfull: Yes(9) No(3)
• usha
  time taken to travel from ranagar to ramgarh=90min
  time taken to travel from ramgarh to rampur=30min
  total time taken =120min=2 hrs.
  2 comes from here @ akhilesh
• 8 years agoHelpfull: Yes(5) No(0)
• PT USHA-
  Ramnagar to ramgarh-
  speed=40 kmph
  time taken= 90 mins
  distance covered=60 km.
  ramgarh to rampur
  dist= 15 km
  time taken =30 mins
  speed= 30 kmph
  rampur to jamnagar-
  speed is 'V'
  Noe,
  shelly maintains speed 18kmph throughout the journey ..distance from ramnagar to rampur =60+15=75 kms.
  time taken by shelly to cover 75 km= 75/18= 4 hours 10 mins.
  Now they reach jamnagar together so the next whole number is 5 so time taken by PT Usha is also 5 hours.
• 8 years agoHelpfull: Yes(4) No(0)
• The speed of Shelly is 18kmph for the entire journey. Since, PT Usha and Shelly started at the same time and finishes also at the same time. So, the average speed of PT Usha is also 18 kmph. PT Usha covered runs for 90 mins at 40kmph (distance = 60 km). Then, covered distance of 15 km in 30 min. At last, assume that distance of x km in t hrs. Speed = distance/time. Overall speed of PT Usha is same as Shelly, i.e., 18kmph. Hence, 18 = (60 + 15 + x)/(3/2 + 1/2 + t). Now, if we start substituting all the options in t, we find that all the options are satisfying equation and condition given in question (of whole number). For Ex. Checking for 41 hrs => t + 3/2 + 1/2 = 41 => t = 39 =>18 = (75 + x)/(2 + 39) => x = 663 => V = x/t = 663/39 = 17. Similarly, A and B also satisfy the equation and condition given in question. Hence, answer is D.
• 8 years agoHelpfull: Yes(3) No(1)
• from where that 60km comes??
  
• 8 years agoHelpfull: Yes(2) No(0)
• 75+v*(n-2)=18*n as distance converted by both of them are equal. All three values satisfies the equation.keep in mind both v and n should be whole numbers.
• 7 years agoHelpfull: Yes(1) No(1)
• The equation must be:
  18n=40*3/2+15+v(n-2)
  18n=60+15+v(n-2)
  So putting n=5,15,41 we get v=5,15,17(whole number)
  So, D must be answer
• 7 years agoHelpfull: Yes(1) No(0)
• Can anyone plz tell me y deepak pandeys solution says 'as n is a natural number the only satisfying number is when v=5 ' ... even if we give values other than 5 to v ,we get natural number values for n.... then how did he conclude that v=5????
• 7 years agoHelpfull: Yes(0) No(0)