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The price of a book was P before any changes. It was increased twice b
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07 Jul 2024, 15:23
07 Jul 2024, 15:23
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The price of a book was P before any changes. It was increased twice by x% each time. Which of the following options are true?
A. The final price of the book after the two successive increases is: P (1 + (x %)^2)
B. The final price of the book after the two successive increases is: P (1+x %)^2
C. The total percentage increase in book’s price after the two successive increases is: 2x + (x %)^2
D. The total percentage increase in the book’s price after the two successive increases is: (2x + (x^2) %) %
A. The final price of the book after the two successive increases is: P (1 + (x %)^2)
B. The final price of the book after the two successive increases is: P (1+x %)^2
C. The total percentage increase in book’s price after the two successive increases is: 2x + (x %)^2
D. The total percentage increase in the book’s price after the two successive increases is: (2x + (x^2) %) %
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The price of a book was P before any changes. It was increased twice b
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07 Dec 2024, 09:45
07 Dec 2024, 09:45
Expert Reply
The price of a book was P before any changes.
We know that the book got two successive increases of $\(x \%\)$ each, so the net percentage change in the price of the book was $\(\left(x+x+\frac{x \times x}{100}\right) \%=\left(2 x+x^2 \%\right) \%\)$
(When there are two successive changes i.e. $\(a \%\)$ & \(b\% \)the net percentage change in their product is of $\(\left(a+b+\frac{a b}{100}\right) \%\)$ )
So, the final price of the book after two successive increases of $\(x \%\)$ each will be $\(\mathrm{P}+\left(2 \mathrm{x}+\mathrm{x}^2 \%\right) \% \times \mathrm{P}=\mathrm{P}\left(1+\left(2 \mathrm{x}+\mathrm{x}^2 \%\right) \%\right)=\mathrm{P}(1+\mathrm{x} \%)^2\)$
Hence options (B) \& (D) are correct.
We know that the book got two successive increases of $\(x \%\)$ each, so the net percentage change in the price of the book was $\(\left(x+x+\frac{x \times x}{100}\right) \%=\left(2 x+x^2 \%\right) \%\)$
(When there are two successive changes i.e. $\(a \%\)$ & \(b\% \)the net percentage change in their product is of $\(\left(a+b+\frac{a b}{100}\right) \%\)$ )
So, the final price of the book after two successive increases of $\(x \%\)$ each will be $\(\mathrm{P}+\left(2 \mathrm{x}+\mathrm{x}^2 \%\right) \% \times \mathrm{P}=\mathrm{P}\left(1+\left(2 \mathrm{x}+\mathrm{x}^2 \%\right) \%\right)=\mathrm{P}(1+\mathrm{x} \%)^2\)$
Hence options (B) \& (D) are correct.
gmatclubot
The price of a book was P before any changes. It was increased twice b [#permalink]
07 Dec 2024, 09:45
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