Latest Elitmus Aptitude Question SOLUTION: 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 distan

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(#M40155981) ELITMUS Numerical Ability question Keep an EYE

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

Asked In Elitmus insha singh (8 years ago)

Solved Deepak Pandey Read Solution (10)

Is this Puzzle helpful?   (18)   (7) Submit Your Solution Time Distance and Speed

Read Solution (10) :

Deepak Pandey  (8 years ago) Best Solution

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

Is this solution Helpfull? Yes (37) | No (9)  

Mohit Gupta  (8 years ago)

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

Is this solution Helpfull? Yes (12) | No (1)  

Akhilesh Kumar Yadav  (8 years ago)

In (n-2) where does 2 comes from@deepak

Is this solution Helpfull? Yes (9) | No (3)  

insha singh  (8 years ago)

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

Is this solution Helpfull? Yes (5) | No   

maths geek  (8 years ago)

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.

Is this solution Helpfull? Yes (4) | No   

Sanjay Singh  (8 years ago)

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.

Is this solution Helpfull? Yes (3) | No (1)  

venkatapriyanka  (8 years ago)

from where that 60km comes??

Is this solution Helpfull? Yes (2) | No   

Poulami   (7 years ago)

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.

Is this solution Helpfull? Yes (1) | No (1)  

Pooja Kumari  (7 years ago)

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

Is this solution Helpfull? Yes (1) | No   

jisa Varghese  (7 years ago)

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????

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