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In year 1980, the price of an article was $X. The price was increased
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03 Jun 2025, 01:59
03 Jun 2025, 01:59
Expert Reply
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In year 1980, the price of an article was $X. The price was increased by 12% from 1980–1982 and the increase in price from 1980–1984 was 24%.
Quantity A |
Quantity B |
Percentage change in price from 1982 - 1984 |
12% |
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Re: In year 1980, the price of an article was $X. The price was increased
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03 Jun 2025, 11:08
03 Jun 2025, 11:08
1
Price in 1980 = x
Price in 1982 = 1.12x
Price in 1984 = 1.24x
Percent change from 1982 to 1984
1.24x - 1.12x/1.12x X 100
- 10.7142...%
Answer choice B
Price in 1982 = 1.12x
Price in 1984 = 1.24x
Percent change from 1982 to 1984
1.24x - 1.12x/1.12x X 100
- 10.7142...%
Answer choice B
Re: In year 1980, the price of an article was $X. The price was increased
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05 Jun 2025, 04:00
05 Jun 2025, 04:00
Expert Reply
Let's denote the prices:
- Price in 1980: $\(P_{1980}=X\)$
- Price in 1982: $\(P_{1982}\)$
- Price in 1984: $\(P_{1984}\)$
Information given:
- 1980-1982 increase: The price increased by $12 \%$ from 1980 to 1982. $\(P_{1982}=P_{1980} \times(1+$ $0.12)=1.12 X\)$
- 1980-1984 increase: The price increased by $24 \%$ from 1980 to 1984. $\(P_{1984}=P_{1980} \times(1+$ $0.24)=1.24 X\)$
Calculate the percentage change from 1982-1984:
The percentage change is calculated as:
$\(\frac{\text { New Price-Old Price }}{\text { Old Price }} \times 100 \%\)$
In this case, the "old price" is $\(P_{1982}\)$ and the "new price" is $\(P_{1984}\)$.
Percentage change $\(=\frac{P_{1984}-P_{1982}}{P_{1982}} \times 100 \%\)$
Percentage change $\(=\frac{1.24 X-1.12 X}{1.12 X} \times 100 \%\)$
Percentage change $\(=\frac{0.12 X}{1.12 X} \times 100 \%\)$
Percentage change $\(=\frac{0.12}{1.12} \times 100 \%\)$
Now, let's calculate the value:
$$
\(\begin{aligned}
& \frac{0.12}{1.12} \approx 0.10714 \\
& 0.10714 \times 100 \%=10.714 \% \text { (approximately) }
\end{aligned}\)
$$
Compare Quantity A and Quantity B:
- Quantity A: Percentage change in price from 1982-1984 $\(\approx 10.714 \%\)$
- Quantity B: $12 \%$
Since $\(10.714 \%<12 \%\)$, Quantity B is greater.
The final answer is $B$
- Price in 1980: $\(P_{1980}=X\)$
- Price in 1982: $\(P_{1982}\)$
- Price in 1984: $\(P_{1984}\)$
Information given:
- 1980-1982 increase: The price increased by $12 \%$ from 1980 to 1982. $\(P_{1982}=P_{1980} \times(1+$ $0.12)=1.12 X\)$
- 1980-1984 increase: The price increased by $24 \%$ from 1980 to 1984. $\(P_{1984}=P_{1980} \times(1+$ $0.24)=1.24 X\)$
Calculate the percentage change from 1982-1984:
The percentage change is calculated as:
$\(\frac{\text { New Price-Old Price }}{\text { Old Price }} \times 100 \%\)$
In this case, the "old price" is $\(P_{1982}\)$ and the "new price" is $\(P_{1984}\)$.
Percentage change $\(=\frac{P_{1984}-P_{1982}}{P_{1982}} \times 100 \%\)$
Percentage change $\(=\frac{1.24 X-1.12 X}{1.12 X} \times 100 \%\)$
Percentage change $\(=\frac{0.12 X}{1.12 X} \times 100 \%\)$
Percentage change $\(=\frac{0.12}{1.12} \times 100 \%\)$
Now, let's calculate the value:
$$
\(\begin{aligned}
& \frac{0.12}{1.12} \approx 0.10714 \\
& 0.10714 \times 100 \%=10.714 \% \text { (approximately) }
\end{aligned}\)
$$
Compare Quantity A and Quantity B:
- Quantity A: Percentage change in price from 1982-1984 $\(\approx 10.714 \%\)$
- Quantity B: $12 \%$
Since $\(10.714 \%<12 \%\)$, Quantity B is greater.
The final answer is $B$
