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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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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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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
= $1.00, Answer A (BTW, Bunuel, I think you signal, cleverly, an odd rule about "less" vs. "fewer" when what we normally think of as countable quantities are involved. Cross pollination for weary brains.) _________________ SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here. Choose life. Senior PS Moderator Joined: 26 Feb 2016 Posts: 3337 Location: India GPA: 3.12 Due to a 25% increase in the price of diesel, a person got 10 liters [#permalink] ### Show Tags 28 Jun 2017, 07:51 Given data : If the price of diesel is x, at 25% more, the price of diesel becomes 1.25x Now from the question stem, if a person gets 10 liters less quantity for 50$ 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: 745 Location: India Concentration: Technology, Strategy 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: 28 Jun 2017 Posts: 7 Re: Due to a 25% increase in the price of diesel, a person got 10 liters [#permalink] ### Show Tags 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. VP Joined: 31 Oct 2013 Posts: 1475 Concentration: Accounting, Finance GPA: 3.68 WE: Analyst (Accounting) Re: Due to a 25% increase in the price of diesel, a person got 10 liters [#permalink] ### Show Tags 24 Sep 2018, 01:43 \sqrt{} 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 Back solve the question . A) 1 No of liters of diesel = 50 /1 = 50 After 25% increase = price = 1.25 50 / 1.25 = 40 Difference is 10. The best answer is A. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 9697 Location: Pune, India Re: Due to a 25% increase in the price of diesel, a person got 10 liters [#permalink] ### Show Tags 24 Sep 2018, 01:53 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 Expense = Amount * Price If price goes up to (5/4) of initial, Amount will go down to (4/5) of initial to keep the expense same. So this 1/5 reduction is 10 lts which means the initial amount was 5*10 = 50 lts Initial price of diesel =$50/50 lts = \$1/lts

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Re: Due to a 25% increase in the price of diesel, a person got 10 liters   [#permalink] 24 Sep 2018, 01:53
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# Due to a 25% increase in the price of diesel, a person got 10 liters

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