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# A reduction in the price of petrol by 10% enables a motorist

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Director
Joined: 03 Sep 2006
Posts: 730
A reduction in the price of petrol by 10% enables a motorist  [#permalink]

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Updated on: 17 Feb 2012, 21:44
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66% (02:15) correct 34% (02:19) wrong based on 342 sessions

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A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $180. Find the original price of petrol? A.$11
B. $5 C.$45
D. $400 E.$4

Originally posted by LM on 17 Feb 2012, 21:29.
Last edited by LM on 17 Feb 2012, 21:44, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 56370

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17 Feb 2012, 22:16
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LM wrote:
A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $180. Find the original price of petrol? A.$11
B. $5 C.$45
D. $400 E.$4

Price decreased by 10%, so 9/10 times, which means that original gallons bought increased 10/9 times. Since this increase equals to 5 gallons then 45 gallons were bought originally (45*10/9=50 --> increase 5 gallons). Hence original price was 180/45=$4. Answer: E. P.S. One can also use backsolving to get the answer. Hope it's clear. _________________ ##### General Discussion Manager Status: May The Force Be With Me (D-DAY 15 May 2012) Joined: 06 Jan 2012 Posts: 198 Location: India Concentration: General Management, Entrepreneurship Re: Percentages-PS [#permalink] ### Show Tags Updated on: 17 Feb 2012, 21:54 I think this is the way to solve it not really sure Let X be no of litres of petrol & n be the price per litre Eqn 1 : x*n = 180 Eqn 2 : (x+5) * (0.9n) = 180 Simplifying eqn 2 0.9xn + 4.5n = 180 Substituting eqn 1 in eqn 2 0.9 ( 180) + 4.5n = 180 n = 18/4.5 = 4 Hence E PS : Thanxs LM for pointing out my error _________________ Giving +1 kudos is a better way of saying 'Thank You'. Originally posted by boomtangboy on 17 Feb 2012, 21:41. Last edited by boomtangboy on 17 Feb 2012, 21:54, edited 1 time in total. Director Joined: 03 Sep 2006 Posts: 730 Re: Percentages-PS [#permalink] ### Show Tags 17 Feb 2012, 21:44 boomtangboy wrote: I think this is the way to solve it not really sure$ 100 - > 100 Litre
$90 -> 105 Litre$180 - > ?

=> 180 * 105 /90 => 210

180/210 => 6/7 => $0.14 / Litre => 210 Litres Please check again, what the question is asking. Director Joined: 03 Sep 2006 Posts: 730 Re: Percentages-PS [#permalink] ### Show Tags 17 Feb 2012, 22:00 1 boomtangboy wrote: I think this is the way to solve it not really sure Let X be no of litres of petrol & n be the price per litre Eqn 1 : x*n = 180 Eqn 2 : (x+5) * (0.9n) = 180 Simplifying eqn 2 0.9xn + 4.5n = 180 Substituting eqn 1 in eqn 2 0.9 ( 180) + 4.5n = 180 n = 18/4.5 = 4 Hence E PS : Thanxs LM for pointing out my error Correct and systematic approach. I was just wondering whether it can be solved within a minute or so without making efforts of too much calculations. Any fast method to solve percentages in such kind of questions? Director Joined: 03 Sep 2006 Posts: 730 Re: Percentages-PS [#permalink] ### Show Tags 17 Feb 2012, 23:12 Bunuel wrote: LM wrote: A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for$180. Find the original price of petrol?

A. $11 B.$5
C. $45 D.$400
E. $4 Price decreased by 10%, so 9/10 times, which means that original gallons bought increased 10/9 times. Since this increase equals to 5 gallons then 45 gallons were bought originally (45*10/9=50 --> increase 5 gallons). Hence original price was 180/45=$4.

P.S. One can also use backsolving to get the answer.

Hope it's clear.

Thanks a lot! How did you quickly arrive at this short method (which I was looking to!) 9/10 decrease will lead to increase of 10/9. This seems to be the key and short cut! Little more explanation or any hint or link within posts would be helpful. Awesome approach!
Math Expert
Joined: 02 Sep 2009
Posts: 56370

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17 Feb 2012, 23:29
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LM wrote:
Thanks a lot! How did you quickly arrive at this short method (which I was looking to!) 9/10 decrease will lead to increase of 10/9. This seems to be the key and short cut! Little more explanation or any hint or link within posts would be helpful. Awesome approach!

Consider this: original price of an item is $10, decrease the price by 50%: new price$5 ($10*1/2=$5). Now, for some fixed amount of money, say for $100, you'll be able to buy twice as many items for$5 (100/$5=20) than for$10 (100/$10=10): reduction in price (1/2) reciprocal of increase in quantity (2) (or simply for half of the price you'll buy twice as many in quantity). The same for the original question. Hope it helps. _________________ Director Joined: 27 May 2012 Posts: 816 Re: A reduction in the price of petrol by 10% enables a motorist [#permalink] ### Show Tags 04 Sep 2012, 08:16 3 LM wrote: A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for$180. Find the original price of petrol?

A. $11 B.$5
C. $45 D.$400
E. $4 initially he got $$x$$ gallons for$180 so 1 gallon = $$\frac{180}{x}$$-- old price per gallon

after reduction of price
he got 5 gallons more , $$x+5$$ gallons for $180 so 1 gallon = $$\frac{180}{x+5}$$----new price per gallon now old price decreased by 10%, so 90% of old price = new price $$(\frac{90}{100})(\frac{180}{x}) = \frac{180}{x+5}$$ --> simplifying $$\frac{162}{x} = \frac{180}{x+5}$$ now solving for x we get x= 45 ,so initially he got 45 gallons for 180 hence price of 1gallon $$\frac{180}{45} = 4$$ _________________ - Stne Manager Joined: 28 Dec 2012 Posts: 99 Location: India Concentration: Strategy, Finance WE: Engineering (Energy and Utilities) Re: A reduction in the price of petrol by 10% enables a motorist [#permalink] ### Show Tags 05 Jan 2013, 03:25 4 LM wrote: A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for$180. Find the original price of petrol?

A. $11 B.$5
C. $45 D.$400
E. $4 Here is a short-cut: Since price decreased by 10% ( i e 1/10) so for same 180$,
quantity increase will be 11.11% (i e 1/9).
So the increase in quantity will be 1/9 of original which is given to be 5.
So original quantity was 5*9 = 45. Thus original price was 180$/45 = 4$.

Concept explanation:

When ever there are problems involving change (like increase decrease) the numerator is either added or substracted from the denominator to change base. Ex. SP = 600$. Profit % = 20%. Now, Profit in$ ? Profit % is calculated on CP.
Profit% = (P*100/CP) but wee are given SP. SO we change the base from CP to SP. 20% of CP = 1/5 of CP = 1/6 of SP = 1/6 of 600 = 100 $. We have added numerator to denominator because new base required is SP, which is larger in case of profit. If it were loss, we would have subtracted. (P/CP )*100% is on base CP (denominator). which can be base changed to SP. SP = P+CP. thus, Profit % can also be shown like (P/(P+CP))*100% I will be posting so more examples soon... hope this helps and add value to this wonderfull site!!! Some kudos please.. I need 50.. am working hard to get them!!! _________________ Impossibility is a relative concept!! Intern Joined: 08 Jan 2013 Posts: 4 Re: A reduction in the price of petrol by 10% enables a motorist [#permalink] ### Show Tags 10 Jan 2013, 12:54 1 I have a slightly different approach where we can directly arrive at the original unit price. Let x be the unit price. We know that we get 5 gallons more after the discount. So the difference is 5. This difference can be expressed as below 180/.9x minus 180/x = 5 where 180/.9x is the no. of gallons we get after discount and 180/x is the no. of gallons we get before discount solving for x gives you 180/45 = 4 Hope this approach helps. thanks, Mohan Senior Manager Joined: 23 Oct 2010 Posts: 337 Location: Azerbaijan Concentration: Finance Schools: HEC '15 (A) GMAT 1: 690 Q47 V38 Re: A reduction in the price of petrol by 10% enables a motorist [#permalink] ### Show Tags 27 Jan 2013, 04:55 3 1 NP=180 0.9P(N+5)=180 0.9P(N+5)=NP N=45 P=180/45=4 _________________ Happy are those who dream dreams and are ready to pay the price to make them come true I am still on all gmat forums. msg me if you want to ask me smth Intern Joined: 09 Oct 2013 Posts: 5 Re: A reduction in the price of petrol by 10% enables a motorist [#permalink] ### Show Tags 21 Oct 2013, 11:58 LM wrote: A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for$180. Find the original price of petrol?

A. $11 B.$5
C. $45 D.$400
E. $4 The question never explicitly states that .9P(X+5) = PX... SVP Joined: 06 Sep 2013 Posts: 1647 Concentration: Finance Re: A reduction in the price of petrol by 10% enables a motorist [#permalink] ### Show Tags 03 Jan 2014, 07:45 1 LM wrote: A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for$180. Find the original price of petrol?

A. $11 B.$5
C. $45 D.$400
E. $4 This is more of a word problem, but anyways One gets (0.9P)(Q+5)=180 Now, once we have this it is better to backsolve. Obviously, D is total out. I'll start with E since answer choices are not in order and I'm guessing GMAT expects me to work in order 180/4 = 45 Replacing in original equaiton one gets (9/10*4)(50) = 180 It matches so answer is E Hope it helps Gimme Kuddos if it does ok? Cheers! J Current Student Status: DONE! Joined: 05 Sep 2016 Posts: 368 Re: A reduction in the price of petrol by 10% enables a motorist [#permalink] ### Show Tags 06 Dec 2016, 18:35 pq=180 0.90p(q+5)=180 0.90pq+4.5p=180 0.90(180)+4.5p=180 4.5p=18 p=4 E. Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2821 Re: A reduction in the price of petrol by 10% enables a motorist [#permalink] ### Show Tags 26 Feb 2018, 10:39 LM wrote: A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for$180. Find the original price of petrol?

A. $11 B.$5
C. $45 D.$400
E. $4 We can let n = the number of gallons normally purchased, and p = the normal price and create the equations: p x n = 180 n = 180/p And 0.9p x (n + 5) = 180 0.9p x (180/p + 5) = 180 162 + 4.5p = 180 4.5p = 18 p = 4 Answer: E _________________ # Jeffrey Miller Head of GMAT Instruction Jeff@TargetTestPrep.com 122 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Intern Joined: 03 Jul 2018 Posts: 1 Re: A reduction in the price of petrol by 10% enables a motorist [#permalink] ### Show Tags 15 Jun 2019, 06:27 10% of 180$ gets us 5 Gallons extra fuel.

18\$ for 5 Gallons >
New Price for one gallon : 18/5

This new price is 90% of original.

(18/5) * (100/90) = Old price = 4
Re: A reduction in the price of petrol by 10% enables a motorist   [#permalink] 15 Jun 2019, 06:27
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