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The cost of gasoline increases by 10%. How many percent must a driver cut back on their gas usage in order to maintain the same expenditure?

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9111 %

9110 %

919 %

None of the above

answer is A.

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Detailed Solution

Given that, the cost of gasoline increases by 10%.
We know that,

D e c r e a s e i n % = D e c r e a s e i n q u a n t i t y o r i g i n a l q u a n t i t y × 100

-(i)
Let the cost of 1unit gasoline usage be Rs ‘x’.
The new cost of 1 unit gasoline after the cost increases by 10% :
New cost of 1unit gasoline,

⇒ R s x + 10 % x

⇒ R s x + 10 x 100 ⇒ R s 100 x + 10 x 100

⇒ R s 110 x 100

New cost of 1 unit gasoline

= R s 11 x 10

.
As mentioned in the question, we want to cut the usage such that expenditure remains same.

Rs . 11 x 10 = 1 unit of gasoline Rs . 1 = 10 11 x unit of gasoline Rs . x = 10 11 x × x units of gasoline Rs . x= 1011 units of gasoline

⇒ 1011 units of gasoline

can be consumed in order to maintain the expenditure.
Decrease in usage,

⇒ 1 − 1011 u n i t s ⇒ 111 u n i t s

(ii)
Now, using (i) & (ii):
Reduction in usage:
Original usage = 1 unit.

⇒ D e c r e a s e i n u s a g e Original u s a g e × 100 % ⇒ 1 / 11 1 × 100 % ⇒ 10011 %

Reduction in usage

= 9111 %

.
Hence, option 1 is correct.

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