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

Question

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

Bunuel · Accepted Answer

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.

sagarsir · Answer

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!!!

LM · Answer

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!

Bunuel · Answer

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.

stne · Answer

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

chvrmohan4 · Answer

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

LalaB · Answer

NP=180
0.9P(N+5)=180

0.9P(N+5)=NP
N=45

P=180/45=4

jlgdr · Answer

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

JeffTargetTestPrep · Answer

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

anvikaraghav · Answer

Hell  Bunuel ,

Can you please explain how did we derive to 45?

Bunuel · Answer

Due to the 10% price reduction, the amount of petrol one could buy increased by a factor of 10/9. If we assume the original amount of petrol purchased was 'x' gallons, then after the price reduction, the amount becomes 'x * 10/9' gallons.

The difference between these two amounts, which is 'x * 10/9 - x', gives us the additional 5 gallons.

When we solve this, we determine that 'x', the original number of gallons bought, was 45.

bumpbot · Answer

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

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