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Due to a 25% increase in the price of diesel, a person got 10 liters

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Due to a 25% increase in the price of diesel, a person got 10 liters  [#permalink]

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New post 28 Jun 2017, 03:29
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Due to a 25% increase in the price of diesel, a person got 10 liters less quantity for $50 than he was getting before the increase. What was the initial price per liter of diesel?

(A) $1.00
(B) $1.50
(C) $2.25
(D) $2.50
(E) $3.00

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Due to a 25% increase in the price of diesel, a person got 10 liters  [#permalink]

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New post 28 Jun 2017, 07:30
Bunuel wrote:
Due to a 25% increase in the price of diesel, a person got 10 liters less quantity for $50 than he was getting before the increase. What was the initial price per liter of diesel?

(A) $1.00
(B) $1.50
(C) $2.25
(D) $2.50
(E) $3.00

Test answer choices. Start with (A) or (E). They have round numbers.

Choice (A). Total price / price per liter = number of liters.

For $50, at $1.00 per liter, \(\frac{50}{1}\) = 50 liters.

A 25% increase in price is $1 * 1.25 = $1.25 per liter.

New quantity at higher price is\(\frac{50}{1.25}\) = 40 liters.

At increased price, she got 10 less liters in quantity. (50-10) = 40. That satisfies the question's condition. Initial price per liter of diesel
= $1.00, Answer A

(BTW, Bunuel, I think you signal, cleverly, an odd rule about "less" vs. "fewer" when what we normally think of as countable quantities are involved. Cross pollination for weary brains.:-))
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Due to a 25% increase in the price of diesel, a person got 10 liters  [#permalink]

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New post 28 Jun 2017, 07:51
Given data :
If the price of diesel is x, at 25% more, the price of diesel becomes 1.25x

Now from the question stem,
if a person gets 10 liters less quantity for 50$ post the increase :
\(\frac{50}{x}- \frac{50}{1.25x} = 10\)
\(\frac{50}{x} - \frac{40}{x} = 10\)
\(\frac{10}{x} = 10\)
Price of diesel(x) = $1(Option A)
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Re: Due to a 25% increase in the price of diesel, a person got 10 liters  [#permalink]

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New post 29 Jun 2017, 05:33
1
Bunuel wrote:
Due to a 25% increase in the price of diesel, a person got 10 liters less quantity for $50 than he was getting before the increase. What was the initial price per liter of diesel?

(A) $1.00
(B) $1.50
(C) $2.25
(D) $2.50
(E) $3.00


Let the initial price of diesel be \(x\), and initial quantity of diesel be \(y\) liters.

Quantity of diesel bought for \($50 => xy = 50\)-------- (i)

Price increased by \(25\)% = \(125\)% of \(x\) \(= \frac{125}{100} * x = 1.25x\)

Quantity of diesel decreased by \(10\) liters \(= (y - 10)\) liters

Quantity of diesel bought for \($50\) after price increase \(=> 1.25x(y - 10) = 50\) -------- (ii)

Equating (i) and (ii), we get;

\(xy = 1.25x(y - 10)\)

\(xy = 1.25xy - 12.5x\)

\(1.25xy - xy = 12.5x\)

\(0.25xy = 12.5x\)

\(0.25y = 12.5\)

\(y = \frac{12.5}{0.25} = 50\)

Therefore initial quantity of diesel, \(y = 50\) liters.

Substituting value of \(y\) in equation (i), we get Initial price \(x\);

\(xy = 50 =>\)\(x*50 = 50\)

\(x = \frac{50}{50} = 1.\)

Therefore Initial price of diesel \(= $1.00\). Answer (A)...
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Due to a 25% increase in the price of diesel, a person got 10 liters  [#permalink]

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New post 30 Jun 2017, 04:02
With 25% increase, price is 62.5
hence 50x = 62.5(x-10)
x = 50, so price per litre is 50/50 = 1 hence (A)
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Re: Due to a 25% increase in the price of diesel, a person got 10 liters  [#permalink]

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New post 30 Jun 2017, 08:46
2
Let the initial price be x. New price would be 1.25x . 1.25x should be a perfect divisor of 50. This is true only for option A. Hence, by elimination answer is A.

Time to solve using this method would be 30 sec max.
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Re: Due to a 25% increase in the price of diesel, a person got 10 liters &nbs [#permalink] 30 Jun 2017, 08:46
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Due to a 25% increase in the price of diesel, a person got 10 liters

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