Question : The price of a scooter increases successively by 10%, 5%, and 15%. What is the total percentage increase in the price of the scooter?
Option 1: $32 \frac{33}{40}$%
Option 2: $34 \frac{21}{40}$%
Option 3: $30 \frac{11}{40}$%
Option 4: $36 \frac{31}{40}$%
Correct Answer: $32 \frac{33}{40}$%
Solution :
Let the initial price of the scooter be 100.
After successive increment of 10%, 5%, and 15%, the price becomes
= $100\times\frac{110}{100}\times\frac{105}{100}\times\frac{115}{100}$
= $100\times\frac{11}{10}\times\frac{21}{20}\times\frac{23}{20}$
= $\frac{11\times21\times23}{40}$
= $\frac{5313}{40}$
Difference = Price after increment – initial price = $\frac{5313}{40}-100=\frac{5313-4000}{40}=\frac{1313}{40}$
$\therefore$ Percentage increased
= $\frac{\text{Difference}}{\text{Initial price}}\times 100$
= $\frac{\frac{1313}{40}}{100}\times 100$
= $\frac{1313}{40}$
= $32 \frac{33}{40}$%
Hence, the correct answer is $32 \frac{33}{40}$%.
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