Latest Elitmus Aptitude Question SOLUTION: PT Usha and Shelly John decided to run a marathon between RamNagar and JamNagar.Both start from RamNagar at 1 Pm. On the way there are two towns RamGadh and Rampur. separated by a

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(#M40018478) ELITMUS question Heights and Distances Keep an EYE

PT Usha and Shelly John decided to run a marathon between RamNagar and JamNagar.Both start from RamNagar at 1 Pm. On the way there are two towns RamGadh and Rampur. separated by a distance of 15KM.PT USHA reaches RamGadh in 90 minutes running at a constant speed of 40 KM/h.She takes additional 30 minutes to reach Rampur,Between Rampur and JamNagar she maintains an average speed of VKm/h.(where v is a whole number).Shelly John being a professional Marathan runner, maintains a constant speed of 18Km/hour.They both reach RamNagar together after n hours n being a whole number.What could be the total time taken by PT USHA??
A)5
B)15
C)41
D)All of the above

Asked In Elitmus Sumit Rawal (11 years ago)

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shweta sharma  (10 years ago)

ramnagar-------60km------ramgrah-------15km-----rampur----(n-2)vkm----jamnagar
let the time taken b n
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
when we will put n=5,that is 75-2v/18-v=5 then v will be =5 km/hr.
and when we will put n=15 ,that is 75-2v/18-v=15.then v will be 15 km/hr.and then we will put 75-2v/18-v=41.then v will be 17km/hr.so 5 ,15,17 all the values of v are satisfying the equation .so answer will be all of the above.

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Sumit Rawal  (11 years ago)

The value of total time taken can be calcultated by using HIT and TRIAL method hint is the value of v is a whole no .
Here total distance between ramnagar and ramgadh =3/2*40=60 Km
Distance b/w RamGadh ANd Rampur is 15 Km
Total distance b/w ramnagar and ramgadh =60+15=75km
toal time taken 75/3/2+1/2=2 hours
Now let the reste of distance i.e b/w Rampur and Jamnagar is xkm
if v is a whole no. and as it is given that speed of shelly john is constant we can formulate eqn
Total time taken by both runners is same
=>75/32.5 +x/v= (75+x)/18..............32.5 -average speed b/w Ramnagar and rampur)
=>x/v=(75+x)/18-2
Put x/v+2=5 then
we get 3=(75+x)/18-2
x=15 and v=5
if we try other cases i.e putting x/v+2=15 or 41 the answer is not coming as whole numbers
Hence 5 is accurate answer

Is this solution Helpfull? Yes (2) | No (9)  

Ravindra  (10 years ago)

all above is the right answer

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shweta sharma  (10 years ago)

all of d above

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zen mano  (11 years ago)

time taken is 5 hours

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Rahul kumar  (10 years ago)

PT usha reached Rampur 2hr before shelly.
nw let pt usha reach Rampur at t
so shelly reach at t-2
nw (t-2)*18=tv
also,t=36/(18-v)
let v =6
therefore t=3
since pt usha took 2 hr to reach rampur,so total time to reach jamnagar=2+3=5

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