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Drogba needs to travel a certain distance.He travels certain distance

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Drogba needs to travel a certain distance.He travels certain distance  [#permalink]

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New post Updated on: 31 Jul 2017, 23:04
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  65% (hard)

Question Stats:

64% (03:25) correct 36% (03:17) wrong based on 69 sessions

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Drogba needs to travel a certain distance.He travels certain distance by car and the rest by train.Car travel costs him $12 per km and traveling by train cost him $8 per km.If the total amount spent on car travel was x% of the total amount spent on the whole journey and the total distance traveled by car was y% of the total distance covered, what is the value of y in terms of x?


A. \(\frac{x}{100-x}\)

B. \(\frac{200x}{300-x}\)

C. \(\frac{300x}{200-x}\)

D. \(\frac{200x}{x-300}\)

E. \(\frac{300x}{100-x}\)

Originally posted by DHAR on 31 Jul 2017, 22:56.
Last edited by Bunuel on 31 Jul 2017, 23:04, edited 1 time in total.
Edited the question.
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Re: A man needs to travel a certain distance. He travels a certain distanc  [#permalink]

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New post 28 Feb 2019, 20:31
kiran120680 wrote:
A man needs to travel a certain distance. He travels a certain distance by car and the rest by train. Car travel costs him $12 per km and traveling by train cost him $8 per km. If the total amount spent on car travel was x% of the total amount spent on whole journey and the total distance travelled by car was y% of the total distance covered, what is the value of y in terms of x?

A. x/(100-x)
B. 200x/(300-x)
C. 300x/(200-x)
D. 200x/(x-300)
E. None of these



The question has already been discussed. Please check before posting..

As for the solution..

Best way would be to take value of x and y
Let the total distance be 100, in which 50% is traveled by each mode, so y=50%.
Total amount spent = 12*50+8*50=1000.
so x = \(\frac{12*50}{1000}\)=60%

Let us check the value that gives us an answer 50%.

A. \(\frac{x}{100-x}=\frac{60}{100-60}=\frac{60}{40}\)...NO

B. \(\frac{200x}{300-x}=\frac{200*60}{300-60}=\frac{12000}{240}=50\)...YES

C. \(\frac{300x}{200-x}=\frac{300*60}{200-60}=\frac{18000}{140}\)...NO

D. \(\frac{200x}{x-300}=\frac{200*60}{60-300}=\frac{12000}{-240}=-50\)... Cannot be negative... NO

E. \(\frac{300x}{100-x}=\frac{300*60}{100-60}=\frac{18000}{40}\) or None of these... NO

Thus B
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Re: Drogba needs to travel a certain distance.He travels certain distance  [#permalink]

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New post 31 Jul 2017, 23:35
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Let the Total distance travelled by Car and Train = 100

Distance Travelled by Car = Y % of 100 = Y
Distance Travelled by Train = (100 - Y) % of 100 = (100 - Y)

Cost incurred with Car Travel = 12 * Y = 12Y
Cost incurred with Train Travel = 8 * (100 - Y) = 800 - 8Y
Total Cost = 12Y + 800 - 8Y = 800 + 4Y = 4 (200 + Y)

Given : Total amount spent on car travel was X% of the total amount spent on the whole journey

\(\frac{12Y * 100}{4 (200 + Y)}\) = X

\(\frac{3Y * 100}{(200 + Y)}\) = X

300Y = 200X + YX

300Y - YX = 200X

Y (300 - X) = 200X

Y = \(\frac{200X}{300 - X}\)

Answer is B
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Re: Drogba needs to travel a certain distance.He travels certain distance  [#permalink]

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New post 31 Jul 2017, 23:05
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DH99 wrote:
Drogba needs to travel a certain distance.He travels certain distance by car and the rest by train.Car travel costs him $12 per km and traveling by train cost him $8 per km.If the total amount spent on car travel was x% of the total amount spent on the whole journey and the total distance traveled by car was y% of the total distance covered, what is the value of y in terms of x?

A. \(\frac{x}{100-x}\)
B. \(\frac{200x}{300-x}\)
C. \(\frac{300x}{200-x}\)
D. \(\frac{200x}{x-300}\)
E. \(\frac{300x}{100-x}\)

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Re: Drogba needs to travel a certain distance.He travels certain distance  [#permalink]

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New post 03 Mar 2019, 03:40
let total distance = 100km
and distance by car = 50 km and train = 50 km
so amount spent on car travel = 12* 50 ; 600 and train 50*8; 400
total 1000
given
x% = 12*50/1000 = 60%
y% = 50/10 = 50%
so now we need to find option where upon doing substitution of x= 60 ; we get y= 50

\(\frac{200x}{300-x}\)
sufficies
IMO B


DHAR wrote:
Drogba needs to travel a certain distance.He travels certain distance by car and the rest by train.Car travel costs him $12 per km and traveling by train cost him $8 per km.If the total amount spent on car travel was x% of the total amount spent on the whole journey and the total distance traveled by car was y% of the total distance covered, what is the value of y in terms of x?


A. \(\frac{x}{100-x}\)

B. \(\frac{200x}{300-x}\)

C. \(\frac{300x}{200-x}\)

D. \(\frac{200x}{x-300}\)

E. \(\frac{300x}{100-x}\)

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Re: Drogba needs to travel a certain distance.He travels certain distance   [#permalink] 03 Mar 2019, 03:40
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