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

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Manager
Joined: 15 Dec 2015
Posts: 115
GMAT 1: 660 Q46 V35
GPA: 4
WE: Information Technology (Computer Software)
Drogba needs to travel a certain distance.He travels certain distance  [#permalink]

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Updated on: 31 Jul 2017, 23:04
9
00:00

Difficulty:

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.
Math Expert
Joined: 02 Aug 2009
Posts: 7737
Re: A man needs to travel a certain distance. He travels a certain distanc  [#permalink]

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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

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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31 Jul 2017, 23:35
3
2
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 = $$\frac{200X}{300 - X}$$

##### General Discussion
Manager
Joined: 15 Dec 2015
Posts: 115
GMAT 1: 660 Q46 V35
GPA: 4
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Re: Drogba needs to travel a certain distance.He travels certain distance  [#permalink]

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31 Jul 2017, 23:05
1
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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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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