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

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Math Expert
Joined: 02 Sep 2009
Posts: 50058
Due to a 25% increase in the price of diesel, a person got 10 liters  [#permalink]

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28 Jun 2017, 03:29
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Difficulty:

35% (medium)

Question Stats:

73% (01:58) correct 27% (02:16) wrong based on 41 sessions

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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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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

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
= $1.00, Answer A (BTW, Bunuel, I think you signal, cleverly, an odd rule about "less" vs. "fewer" when what we normally think of as countable quantities are involved. Cross pollination for weary brains.) _________________ ___________________________________________________________________ For what are we born if not to aid one another? -- Ernest Hemingway Senior PS Moderator Joined: 26 Feb 2016 Posts: 3207 Location: India GPA: 3.12 Due to a 25% increase in the price of diesel, a person got 10 liters [#permalink] ### Show Tags 28 Jun 2017, 07:51 Given data : If the price of diesel is x, at 25% more, the price of diesel becomes 1.25x Now from the question stem, if a person gets 10 liters less quantity for 50$ 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) _________________ You've got what it takes, but it will take everything you've got Director Joined: 04 Dec 2015 Posts: 701 Location: India Concentration: Technology, Strategy Schools: ISB '19, IIMA , IIMB, XLRI WE: Information Technology (Consulting) Re: Due to a 25% increase in the price of diesel, a person got 10 liters [#permalink] ### Show Tags 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)...
Intern
Joined: 01 May 2017
Posts: 4
Due to a 25% increase in the price of diesel, a person got 10 liters  [#permalink]

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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)
Intern
Joined: 28 Jun 2017
Posts: 7
Re: Due to a 25% increase in the price of diesel, a person got 10 liters  [#permalink]

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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.
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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