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Recently, fuel price has seen a hike of 20%. Mr X is planning to buy

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Recently, fuel price has seen a hike of 20%. Mr X is planning to buy [#permalink]

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Recently, fuel price has seen a hike of 20%. Mr X is planning to buy a new car with better mileage as compared to his current car. By what % should the new mileage be more than the previous mileage to ensure that Mr X’s total fuel cost stays the same for the month? (assuming the distance traveled every month stays the same)[/b]

(A) 10%
(B) 17%
(C) 20%
(D) 21%
(E) 25%
[Reveal] Spoiler: OA

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Recently, fuel price has seen a hike of 20%. Mr X is planning to buy [#permalink]

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New post 07 Jul 2017, 03:18
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Bunuel wrote:
Recently, fuel price has seen a hike of 20%. Mr X is planning to buy a new car with better mileage as compared to his current car. By what % should the new mileage be more than the previous mileage to ensure that Mr X’s total fuel cost stays the same for the month? (assuming the distance traveled every month stays the same)[/b]

(A) 10%
(B) 17%
(C) 20%
(D) 21%
(E) 25%


Answer: B
Lets say Price and Mileage before hike are P1 and M1 respectively. After Hike, they are P2 and M2 respectively.

If price per mile is to stay the same, we need to have this equation.

\(P1 / M1 = P2 / M2\)

\(M2 = P2 * M1/P1\)

but P2 is 1.2 times P1.

\(P1 / M1 = 1.2P1 / M2 * P1\)

\(M2 = 1.2M1\)

Difference is 1.2 or 20%.

Edit: Editing after mistake was pointed out by chetan2u
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Last edited by jedit on 07 Jul 2017, 20:51, edited 2 times in total.

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Recently, fuel price has seen a hike of 20%. Mr X is planning to buy [#permalink]

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New post 07 Jul 2017, 03:42
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jedit wrote:
Bunuel wrote:
Recently, fuel price has seen a hike of 20%. Mr X is planning to buy a new car with better mileage as compared to his current car. By what % should the new mileage be more than the previous mileage to ensure that Mr X’s total fuel cost stays the same for the month? (assuming the distance traveled every month stays the same)[/b]

(A) 10%
(B) 17%
(C) 20%
(D) 21%
(E) 25%


Answer: B
Lets say Price and Mileage before hike are P1 and M1 respectively. After Hike, they are P2 and M2 respectively.

We need them to be Equal.

\(P1 * M1 = P2 * M2\)



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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Re: Recently, fuel price has seen a hike of 20%. Mr X is planning to buy [#permalink]

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New post 07 Jul 2017, 19:30
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.

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Re: Recently, fuel price has seen a hike of 20%. Mr X is planning to buy [#permalink]

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Total cost initially = C * fuel => C * Distance/mileage ( mileage = distance/litre)
Let initial mileage be m1 and later mileage be m2
Later cost = 1.2C* Distance/m2
Cost has to remain same => C*D/m1 = 1.2 C* D/m2
=>m2 = 1.2m1 => 20% increase in mileage
IMO C

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Re: Recently, fuel price has seen a hike of 20%. Mr X is planning to buy [#permalink]

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New post 10 Jul 2017, 23:09
Confused like a chameleon in a bag of Skittles! Please help with an alternative explanation :)

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Re: Recently, fuel price has seen a hike of 20%. Mr X is planning to buy [#permalink]

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New post 12 Jul 2017, 16:36
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Bunuel wrote:
Recently, fuel price has seen a hike of 20%. Mr X is planning to buy a new car with better mileage as compared to his current car. By what % should the new mileage be more than the previous mileage to ensure that Mr X’s total fuel cost stays the same for the month? (assuming the distance traveled every month stays the same)[/b]

(A) 10%
(B) 17%
(C) 20%
(D) 21%
(E) 25%


Since the fuel price is directly proportional to mileage of a car; if the fuel price is increased by 20%, the mileage of the car should be increased by 20% as well to keep the total fuel cost the same.

Answer: C
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Re: Recently, fuel price has seen a hike of 20%. Mr X is planning to buy [#permalink]

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New post 20 Jul 2017, 05:10
chetan2u wrote:
jedit wrote:
Bunuel wrote:
Recently, fuel price has seen a hike of 20%. Mr X is planning to buy a new car with better mileage as compared to his current car. By what % should the new mileage be more than the previous mileage to ensure that Mr X’s total fuel cost stays the same for the month? (assuming the distance traveled every month stays the same)[/b]

(A) 10%
(B) 17%
(C) 20%
(D) 21%
(E) 25%


Answer: B
Lets say Price and Mileage before hike are P1 and M1 respectively. After Hike, they are P2 and M2 respectively.

We need them to be Equal.

\(P1 * M1 = P2 * M2\)



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 P1/M1=P2/M2.......m2=p2*m1p1
Ans 20%
C


Hi Chetan2u,

I guess you mentioned to say, m2 = p2*(m1/p1)

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Re: Recently, fuel price has seen a hike of 20%. Mr X is planning to buy [#permalink]

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New post 30 Aug 2017, 09:26
jedit wrote:
Bunuel wrote:
Recently, fuel price has seen a hike of 20%. Mr X is planning to buy a new car with better mileage as compared to his current car. By what % should the new mileage be more than the previous mileage to ensure that Mr X’s total fuel cost stays the same for the month? (assuming the distance traveled every month stays the same)[/b]

(A) 10%
(B) 17%
(C) 20%
(D) 21%
(E) 25%


Answer: B
Lets say Price and Mileage before hike are P1 and M1 respectively. After Hike, they are P2 and M2 respectively.

If price per mile is to stay the same, we need to have this equation.

\(P1 / M1 = P2 / M2\)

\(M2 = P2 * M1/P1\)

but P2 is 1.2 times P1.

\(P1 / M1 = 1.2P1 / M2 * P1\)

\(M2 = 1.2M1\)

Difference is 1.2 or 20%.

Edit: Editing after mistake was pointed out by chetan2u


hi

okay with your solution ...

can you, however, apply the same logic to the following problem ....??

The cost of fuel increases by 10%. By what % must the consumption of fuel decrease to keep the overall amount spent on the fuel same?

(A) 5%
(B) 9%
(C) 10%
(D) 11%
(E) 20%

thanks in advance ...

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Recently, fuel price has seen a hike of 20%. Mr X is planning to buy [#permalink]

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New post 13 Sep 2017, 08:18
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.

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Recently, fuel price has seen a hike of 20%. Mr X is planning to buy [#permalink]

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New post 13 Sep 2017, 08:40
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This problem becomes a lot easier when we assume numbers.

If we were buying 1 unit fuel worth 100$ and the old car was
offering a mileage of 10 miles/gallon, it would cost us 10$ to drive a mile

Since the price has gone up by 20%, the fuel will now cost 120$.
If he needs to spend the same amount per miles driven,

Let the mileage of the new car be x

Therefore, \(\frac{120}{x} = 10\)
\(x = 12\)(which is a 20% increase over 10$/galon) (Option C)
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