A reduction in the price of petrol by 10% enables...

LUANDATO wrote:A motorist spends $180 on gas. If the cost per gallon had been 10% less, then for the same $180, the motorist would have been able to purchase 5 more gallons of gas than he had purchased initially. What was the original cost per gallon of gas?

A. $11
B. $5
C. $45
D. $400
E. $4

The OA is E.

I'm really confused by this PS question. Experts, any suggestion about how can I solve it? Thanks in advance.

Aside: I cleaned up the wording of the question to make it clearer.

Note that the unit cost and quantity will have a reciprocal relationship. If the unit cost were to double, you could buy half as much gas for the same total outlay.

Thus, if the cost decreased by 10%, the new cost would be .9, or 9/10 of the old cost.
If cost and quantity have a reciprocal relationship, then the new quantity of gas would be 10/9, or 1 + 1/9 of the old quantity. Put another way, the old quantity was increased by 1/9.
If 5 gallons represents a 1/9 increase, and we call the old quantity 'q' then (1/9)q = 5 --> q = 45.
If the old quantity was 45 gallons, and the motorist paid $180, the old cost was 180/45 = 4. The answer is E

A motorist spends $180 on gas. If the cost per gallon had been 10% less, then for the same $180, the motorist would have been able to purchase 5 more gallons of gas than he had purchased initially. What was the original cost per gallon of gas?

A. $11
B. $5
C. $45
D. $400
E. $4

The OA is E.

I'm really confused by this PS question. Experts, any suggestion about how can I solve it? Thanks in advance.

And there's always good-old-fashioned back-solving.

Test B. If the old price were $5, the old quantity would have been 180/5 = 36 gallons.
If the price decreased by 10%, the new price would be $4.50, and the new quantity would be 180/4.5 = 40 gallons.
Thus, the motorist could have purchased 40-36 = 4 more gallons. It should actually be 5. So B is out.

(Notice now that you're close to the correct answer. The only other answer choice that makes sense is E. You don't really need to test it.

But for fun....

If old cost were $4, the old quantity would have been 180/4 = 45 gallons
If the cost decreased by 10%, the new cost would be $3.60, and the new quantity would be 180/3.6 = 50
50 -45 = 5 gallons. And we're done. The answer is E