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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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Difficulty:   55% (hard)

Question Stats: 66% (02:15) correct 34% (02:19) wrong based on 342 sessions

### HideShow timer Statistics 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 V
Joined: 02 Sep 2009
Posts: 56370

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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=$4. Answer: E. P.S. One can also use backsolving to get the answer. Hope it's clear. _________________ ##### General Discussion Manager  B Status: May The Force Be With Me (D-DAY 15 May 2012) Joined: 06 Jan 2012 Posts: 198 Location: India Concentration: General Management, Entrepreneurship Re: Percentages-PS [#permalink] ### Show Tags I think this is the way to solve it not really sure Let X be no of litres of petrol & n be the price per litre Eqn 1 : x*n = 180 Eqn 2 : (x+5) * (0.9n) = 180 Simplifying eqn 2 0.9xn + 4.5n = 180 Substituting eqn 1 in eqn 2 0.9 ( 180) + 4.5n = 180 n = 18/4.5 = 4 Hence E PS : Thanxs LM for pointing out my error _________________ Giving +1 kudos is a better way of saying 'Thank You'. Originally posted by boomtangboy on 17 Feb 2012, 21:41. Last edited by boomtangboy on 17 Feb 2012, 21:54, edited 1 time in total. Director  Joined: 03 Sep 2006 Posts: 730 Re: Percentages-PS [#permalink] ### Show Tags boomtangboy wrote: I think this is the way to solve it not really sure$ 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 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 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 V
Joined: 02 Sep 2009
Posts: 56370

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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  V Joined: 27 May 2012 Posts: 816 Re: A reduction in the price of petrol by 10% enables a motorist [#permalink] ### Show Tags 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 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 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 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 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 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 B Status: DONE! Joined: 05 Sep 2016 Posts: 368 Re: A reduction in the price of petrol by 10% enables a motorist [#permalink] ### Show Tags 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 G 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 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. $4 We can let n = the number of gallons normally purchased, and p = the normal price and create the equations: p x n = 180 n = 180/p And 0.9p x (n + 5) = 180 0.9p x (180/p + 5) = 180 162 + 4.5p = 180 4.5p = 18 p = 4 Answer: E _________________ # Jeffrey Miller Head of GMAT Instruction Jeff@TargetTestPrep.com See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Intern  B Joined: 03 Jul 2018 Posts: 1 Re: A reduction in the price of petrol by 10% enables a motorist [#permalink] ### Show Tags 10% of 180$ 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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