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The price of a piece of land in Pokhara was fixed at Rs [tex]1,20,00,000[/tex] at the end of 2020 AD. The price increased by [tex]10 \%[/tex] as a consequence of increasing buying pressure at the beginning of 2021. But the price of land decreased by [tex]4 \%[/tex] due to the economic crisis at the end of 2022 AD.

(a) चलन चल्तीको सङकेतअनुसार [tex]P \left(1+\frac{ R }{100}\right)^{ T }[/tex] ले के जनाउँछ?
(What does [tex]P \left(1+\frac{ R }{100}\right)^{ T }[/tex] as per usual notation indicate?)

(b) ई.सं. 2020 मा 1 आना जग्गाको मूल्य पत्ता लगाउनुहोस्।
(Find the price of 1 Aana land in the year 2020 AD.)

(c) 2022 को अन्त्यमा सो घडेरीको मूल्य कति भए होला, पत्ता लगाउनुहोस्।
(What will be the price of the land at the end of 2022?)

(d) ई. सं. 2022 मा [tex]4 \%[/tex] ले घट्नुको साटो [tex]5 \%[/tex] ले घटेको भए जग्गा बेच्ने मानिसलाई कति घाटा हुन्थ्यो होला, गणना गरी पत्ता लगाउनुहोस्।
(How much loss would there be to the person if the price decreased by [tex]5 \%[/tex] instead of decreasing by [tex]4 \%[/tex] in 2022 AD?)

Ans:
(a) Price after [tex]T[/tex] years
(b) Rs [tex]30,00,000[/tex]
(c) Rs [tex]1,26,72,000[/tex]
(d) Rs [tex]1,20,00,000 \times 0.96 \times 0.95 = Rs 1,09,44,000[/tex]

Sagot :

GinnyAnswer
Let's break down the solution step-by-step:

### (a) चलन चल्तीको सङकेतअनुसार [tex]\(P \left(1+\frac{ R }{100}\right)^{ T }\)[/tex] ले के जनाउँछ ?
What does [tex]\( P \left(1+\frac{ R }{100}\right)^{ T } \)[/tex] as per usual notation indicate?

This formula is used to calculate the compounded price of an asset over time, considering a growth rate [tex]\( R \)[/tex] over [tex]\( T \)[/tex] time periods.

- [tex]\( P \)[/tex] represents the initial price or principal amount.
- [tex]\( R \)[/tex] represents the rate of increase or decrease per time period (usually given as a percentage).
- [tex]\( T \)[/tex] is the number of time periods (often in years).

So, [tex]\( P \left(1+\frac{ R }{100}\right)^{ T } \)[/tex] indicates the price of the asset after [tex]\( T \)[/tex] years given a yearly rate [tex]\( R \)[/tex].

### (b) ई.सं. 2020 मा 1 आना जगगाको मूल्य पत्ता लगाउनुहोस् ।
Find the price of 1 Aana land in the year 2020 AD.

Given that the total price of the land at the end of 2020 is Rs [tex]\( 1,20,00,000 \)[/tex] and it encompasses 4 Aanas, we can calculate the price of 1 Aana:

[tex]\[ \text{Price of 1 Aana} = \frac{1,20,00,000}{4} = 30,00,000 \, \text{Rs} \][/tex]

Hence, the price of 1 Aana land in 2020 AD is Rs 30,00,000.

### (c) 2022 को अन्त्यमा सो घडेरीको मूल्य कति भए होला, पत्ता लगाउनुहोस् ।
What will be the price of the land at the end of 2022?

Initially, the price of the land at the end of 2020 is Rs 1,20,00,000. In 2021, the price increased by [tex]\(10 \%\)[/tex].

First, calculate the price at the end of 2021:
[tex]\[ \text{Price at the end of 2021} = 1,20,00,000 \times \left(1 + \frac{10}{100}\right) = 1,20,00,000 \times 1.10 = 1,32,00,000 \, \text{Rs} \][/tex]

Next, calculate the price at the end of 2022 after a [tex]\(4 \%\)[/tex] decrease:
[tex]\[ \text{Price at the end of 2022} = 1,32,00,000 \times \left(1 - \frac{4}{100}\right) = 1,32,00,000 \times 0.96 = 1,26,72,000 \, \text{Rs} \][/tex]

So, the price of the land at the end of 2022 is Rs 1,26,72,000.

### (d) ई. सं. 2022 मा [tex]\(4 \%\)[/tex] ले घट्नुको साटो [tex]\(5 \%\)[/tex] ले घटेको भए जग्गा बेच्ने मानिसलाई कति घाटा हुन्थ्यो होला, गणना गरी पत्ता लगाउनुहोस्
How much loss will be there to the person if the price decreased by [tex]\(5 \%\)[/tex] instead of decreasing by [tex]\(4 \%\)[/tex] in 2022 AD?

First, calculate the price at the end of 2022 if the price decreased by [tex]\(5 \%\)[/tex]:
[tex]\[ \text{Price at the end of 2022 with 5\% decrease} = 1,32,00,000 \times \left(1 - \frac{5}{100}\right) = 1,32,00,000 \times 0.95 = 1,25,40,000 \, \text{Rs} \][/tex]

Now, calculate the difference between the price with a [tex]\(4 \%\)[/tex] decrease and a [tex]\(5 \%\)[/tex] decrease to find the loss:
[tex]\[ \text{Loss} = \text{Price with 4\% decrease} - \text{Price with 5\% decrease} \][/tex]
[tex]\[ \text{Loss} = 1,26,72,000 - 1,25,40,000 = 1,32,000 \, \text{Rs} \][/tex]

Hence, if the price decreased by [tex]\(5 \%\)[/tex] instead of [tex]\(4 \%\)[/tex] in 2022, the loss to the person would be Rs 1,32,000.
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