A man needs to travel a certain distance. He travels certain distance

Question

A man 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 travelling by train costs 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 traveled 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

A. x/(100-x)

B. 200x/(300-x)

C. 300x/(200-x)

D. 200x/(x-300)

E. None of these

GM10 · Answer

Bunuel   VeritasKarishma  can you please help with the above question?

Thanks

Kinshook · Answer

Given: A man 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 travelling by train costs him $8 per km.

Asked: If the total amount spent on car travel was x% of the total amount spent on 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?

Let the man travel c km by car and t km by train.

Costs: - 
Cost of travel by car = 12c
Cost of travel by train = 8t
12c = x% (12c + 8t)
12c (1-x%) = x%8t
c/t = 2x%/3(1-x%)

Distance: - 
Cost of travel by car = c
Cost of travel by train = t
c = y% (c + t)
c(1-y%) = y%t
c/t = y%/(1-y%)

2x%/3(1-x%) = y%/(1-y%)
y% = 2x%/{2x% + 3(1-x%)} = 2x%/(3 -x%) = 2x/(300-x)
y = 200x/(300-x)

IMO B

KarishmaB · Answer

Assume values.

Cost by car = $12/km
Cost by train = $8/km

So say 1 km was travelled by car and 1 km by train. So total 2 kms were covered for $20 such that cost by car was $12 which is 60% of total expense. So x = 60.
Distance covered by car was 1 km out of 2 km so 50% of the total distance. So y = 50.

In the options, put x = 60 and look for the option that gives 50. 
Only option (B) does.

In GMAT questions, 'none of these' is not an option so there wouldn't be any problem.

KarishmaB · Answer

Alternatively, assuming total distance travelled as 100, y will be travelled by car and (100 - y) by train. So total cost by car will be 12y and that by train will be 8(100 - y)

\frac{x}{100} = \frac{12y}{12y + 8(100 - y)}

\frac{100}{x} = \frac{12y + 8(100 - y)}{12y}

\frac{1200}{x} = \frac{4y + 800}{y}

\frac{1200-4x}{x} = \frac{800}{y}

y = \frac{200x}{300-x}

Answer (B)

FanCC · Answer

Here's my approach.

Car's Cost: x%
Train's Cost: 1-x%

Car's Distance: y%
y% = Car's Distance/Total distance x 100%

Total distance: x%/12 + (1-x%)/8
Car's Distance : x%/12

Put them together: y % = (x%/12)/   
Simplify: y%= 2x/(300-x), 
Finalize: y = 200x/(300-x)

luisdicampo · Answer

Deconstructing the Question  
Car Cost = $12/km.
Train Cost = $8/km.
Given:
1. Car Cost is  x\%  of Total Cost.
2. Car Distance is  y\%  of Total Distance.
Target: Find  y  in terms of  x .

Step 1: Set up Variables (or Smart Numbers)  
Let Total Distance = 100 units (to make percentages easy).
Then:
- Distance by Car =  y 
- Distance by Train =  100 - y

Step 2: Calculate Costs  
- Cost by Car ( C_c ) =  12 	imes y = 12y 
- Cost by Train ( C_t ) =  8 	imes (100 - y) = 800 - 8y 
- Total Cost ( C_{tot} ) =  12y + 800 - 8y = 4y + 800

Step 3: Relate to x  
We are given that  C_c  is  x\%  of  C_{tot} .
Equation:
 \frac{C_c}{C_{tot}} = \frac{x}{100} 
 \frac{12y}{4y + 800} = \frac{x}{100}

Simplify the left side by dividing numerator and denominator by 4:
 \frac{3y}{y + 200} = \frac{x}{100}

Step 4: Solve for y  
Cross-multiply:
 300y = x(y + 200) 
 300y = xy + 200x

Rearrange to isolate  y :
 300y - xy = 200x 
 y(300 - x) = 200x 
 y = \frac{200x}{300 - x}

Answer:  B

egmat · Answer

Step 1: Set up what we know 
- Car travel:  $12  per km
- Train travel:  $8  per km
- Car cost =  x%  of total cost
- Car distance =  y%  of total distance (we need to find this)

Step 2: Use percentages to write equations 
If car distance is  y%  of total distance:
- Car distance =  (y/100) × Total Distance 
- Train distance =  ((100-y)/100) × Total Distance

Step 3: Write the cost equation 
Car cost =  x%  of total cost means:
 12 × Car distance = (x/100) × (Car cost + Train cost)

Substituting:
 12 × (y/100) × D = (x/100) ×

Step 4: Simplify (divide by D and multiply by 100) 
12y = x ×  
12y = x ×  
12y = x ×  
1200y = x(4y + 800)
1200y = 4xy + 800x
1200y - 4xy = 800x
y(1200 - 4x) = 800x

Therefore: 
 y = 800x/(1200 - 4x) = 800x/  = 200x/(300 - x)

Answer: B. 200x/(300-x)

A man needs to travel a certain distance. He travels certain distance

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