Hi..
We have to be very careful while making the equation
Even the Q tells you that the new mileage INCREASE, so the increase cannot be together both in P and M as the equation taken by you..

What is mileage? D/L...
D is same ..

So \(\frac{P_1}{M_1}=\frac{P_2}{M_2}.......m_2=\frac{p_2*m_1}{p_1}\)
Ans 20%
C
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lets take 1 gallon of gas - 10$ - gives 30miles
same eq : 1 gallon of gas - 12$ - give x miles to breakeven.
12*30/10 = 36 , so miles should increase by 6 means 20% increase.
Ans C.

Confused like a chameleon in a bag of Skittles! Please help with an alternative explanation

Hi Chetan2u,

I guess you mentioned to say, m2 = p2*(m1/p1)
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Let's assume you can drive 100 miles at a cost of 1000 usd.
Because of the price increase, you now have to spend 1200 usd to drive the same mileage.

That means you used to spend 10 usd per mile, now you spend 12.

So, let M2 be the requested mileage so that the price per mile remains at 10 usd:

\(1200/M2 = 10\)

\(M2 = 120\)

\((120-100)/100 = 0.2\)

Thus answer C is the right one.

Make sense ^^
Thank you for your explanation +1 Kudos

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This can be seen as a problem with 2 inverse variations:
1. Since Mr.X want to be keep his fuel cost = const , the fuel hike would mean low fuel consumption i.e
cost = fuel price * fuel consumption = constant
after 20% hike, new fuel price = (fuel price)*(120/100) ---(a)
(fuel price) * (fuel consumption) = (new fuel price)*(fuel consumption)
On substituting (a) in the above, we get:
=> new fuel consumption = (fuel consumption) 100/120 {meaning fuel consumption has decreased now)

2. Next is about mileage, now Mr.X wants better mileage to handle the decreased fuel consumption

(old Mileage) * (fuel consumption) = (new mileage) * (new fuel consumption)

since new fuel consumption = (fuel consumption) 100/120

new mileage = (old mileage) * 120/100 => indicating a 20 % increase needed in mileage

TL;DR

Total Cost ($) = Unit Price ($/unit) * Quantity (units)
Cost ($) = Fuel Price ($/litre) * 1/Mileage (litre/km) * Distance (km)

1 = (6/5) * 1/m * 1 => m = 6/5
Increase in m = 6/5 - 1 = 1/5 = 20%

ANSWER: C

Veritas Prep Official Solution

The problem here is ‘how is mileage related to fuel price?’

Total fuel cost = Fuel price * Quantity of fuel used

Since the ‘total fuel cost’ needs to stay the same, ‘fuel price’ varies inversely with ‘quantity of fuel used’.

Quantity of fuel used = Distance traveled/Mileage

Distance traveled = Quantity of fuel used*Mileage

Since the same distance needs to be traveled, ‘quantity of fuel used’ varies inversely with the ‘mileage’.

We see that ‘fuel price’ varies inversely with ‘quantity of fuel used’ and ‘quantity of fuel used’ varies inversely with ‘mileage’. So, if fuel price increases, quantity of fuel used decreases proportionally and if quantity of fuel used decreases, mileage increases proportionally. Hence, if fuel price increases, mileage increases proportionally or we can say that fuel price varies directly with mileage.

If fuel price becomes 6/5 (20% increase) of previous fuel price, we need the mileage to become 6/5 of the previous mileage too i.e. mileage should increase by 20% too.

Another method is that you can directly plug in the expression for ‘Quantity of fuel used’ in the original equation.

Total fuel cost = Fuel price * Distance traveled/Mileage

Since ‘total fuel cost’ and ‘distance traveled’ need to stay the same, ‘fuel price’ is directly proportional to ‘mileage’.

Answer (C)
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How correct we can set a general rule for the variation concept as following :
Direct proportion relation between two measurements, so it requires the same increase or decrease percentage
to retain the direct proportion relation. As for the inversely proportional measurements to each other, the reciprocal of the increase / decrease fraction for the same purpose is highly needed.

Who agree with me for the in general sense. For sure tricky and special cases need us to manipulate far beyond such general rule to correctly solve the problem