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!!!

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