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Sagot :
Let's address each part of the question step-by-step:
(a) चक्रीय मिश्रह्हास पत्ता लगाउने सूत्र लेखनुहोस् ।
To find the formula for compound depreciation, we use a similar formula to compound interest, but instead of adding interest, we subtract depreciation. The formula is:
[tex]\[ P_T = P \left(1 - \frac{R}{100}\right)^T \][/tex]
where:
- [tex]\( P_T \)[/tex] is the depreciated value after [tex]\( T \)[/tex] years,
- [tex]\( P \)[/tex] is the initial value,
- [tex]\( R \)[/tex] is the rate of depreciation per year (as a percentage),
- [tex]\( T \)[/tex] is the number of years.
(b) चक्रीय ह्वासदर पत्ता लगाउनुहोस् ।
To find the rate of compound depreciation ([tex]\( R \)[/tex]), we use the given information that the value of the mobile is Rs. 16,928 after 2 years and Rs. 15,573.76 after 3 years.
We can set up the following equations based on the formula:
[tex]\[ 16928 = P \left(1 - \frac{R}{100}\right)^2 \][/tex]
[tex]\[ 15573.76 = P \left(1 - \frac{R}{100}\right)^3 \][/tex]
To eliminate the initial price [tex]\( P \)[/tex], we divide the second equation by the first:
[tex]\[ \frac{15573.76}{16928} = \left(1 - \frac{R}{100}\right)^{3-2} \][/tex]
[tex]\[ \frac{15573.76}{16928} = \left(1 - \frac{R}{100}\right) \][/tex]
By solving the above:
[tex]\[ \left(1 - \frac{R}{100}\right) = \frac{15573.76}{16928} \][/tex]
To find [tex]\( R \)[/tex]:
[tex]\[ \frac{15573.76}{16928} = 0.92 \][/tex] (approx.)
Therefore:
[tex]\[ 1 - \frac{R}{100} = 0.92 \][/tex]
[tex]\[ \frac{R}{100} = 0.08 \][/tex]
[tex]\[ R = 8\% \][/tex]
(c) उक्त मोबाइल सेटलाई सुरुमा कतिमा किनिएको थियो।
Now, we need to find the initial cost [tex]\( P \)[/tex]. Using the formula and the given value after 2 years:
[tex]\[ 16928 = P \left(1 - \frac{8}{100}\right)^2 \][/tex]
[tex]\[ 16928 = P \left(0.92\right)^2 \][/tex]
[tex]\[ 16928 = P \cdot 0.8464 \][/tex]
Solving for [tex]\( P \)[/tex]:
[tex]\[ P = \frac{16928}{0.8464} \][/tex]
[tex]\[ P = 20000 \][/tex]
Therefore, the initial cost of the mobile set was Rs. 20,000.
So, the detailed results are:
(a) The formula for compound depreciation is:
[tex]\[ P_T = P \left(1 - \frac{R}{100}\right)^T \][/tex]
(b) The rate of compound depreciation ([tex]\( R \)[/tex]) is:
[tex]\[ 8\% \][/tex]
(c) The initial cost of the mobile set ([tex]\( P \)[/tex]) is:
[tex]\[ \text{Rs.} 20,000 \][/tex]
(a) चक्रीय मिश्रह्हास पत्ता लगाउने सूत्र लेखनुहोस् ।
To find the formula for compound depreciation, we use a similar formula to compound interest, but instead of adding interest, we subtract depreciation. The formula is:
[tex]\[ P_T = P \left(1 - \frac{R}{100}\right)^T \][/tex]
where:
- [tex]\( P_T \)[/tex] is the depreciated value after [tex]\( T \)[/tex] years,
- [tex]\( P \)[/tex] is the initial value,
- [tex]\( R \)[/tex] is the rate of depreciation per year (as a percentage),
- [tex]\( T \)[/tex] is the number of years.
(b) चक्रीय ह्वासदर पत्ता लगाउनुहोस् ।
To find the rate of compound depreciation ([tex]\( R \)[/tex]), we use the given information that the value of the mobile is Rs. 16,928 after 2 years and Rs. 15,573.76 after 3 years.
We can set up the following equations based on the formula:
[tex]\[ 16928 = P \left(1 - \frac{R}{100}\right)^2 \][/tex]
[tex]\[ 15573.76 = P \left(1 - \frac{R}{100}\right)^3 \][/tex]
To eliminate the initial price [tex]\( P \)[/tex], we divide the second equation by the first:
[tex]\[ \frac{15573.76}{16928} = \left(1 - \frac{R}{100}\right)^{3-2} \][/tex]
[tex]\[ \frac{15573.76}{16928} = \left(1 - \frac{R}{100}\right) \][/tex]
By solving the above:
[tex]\[ \left(1 - \frac{R}{100}\right) = \frac{15573.76}{16928} \][/tex]
To find [tex]\( R \)[/tex]:
[tex]\[ \frac{15573.76}{16928} = 0.92 \][/tex] (approx.)
Therefore:
[tex]\[ 1 - \frac{R}{100} = 0.92 \][/tex]
[tex]\[ \frac{R}{100} = 0.08 \][/tex]
[tex]\[ R = 8\% \][/tex]
(c) उक्त मोबाइल सेटलाई सुरुमा कतिमा किनिएको थियो।
Now, we need to find the initial cost [tex]\( P \)[/tex]. Using the formula and the given value after 2 years:
[tex]\[ 16928 = P \left(1 - \frac{8}{100}\right)^2 \][/tex]
[tex]\[ 16928 = P \left(0.92\right)^2 \][/tex]
[tex]\[ 16928 = P \cdot 0.8464 \][/tex]
Solving for [tex]\( P \)[/tex]:
[tex]\[ P = \frac{16928}{0.8464} \][/tex]
[tex]\[ P = 20000 \][/tex]
Therefore, the initial cost of the mobile set was Rs. 20,000.
So, the detailed results are:
(a) The formula for compound depreciation is:
[tex]\[ P_T = P \left(1 - \frac{R}{100}\right)^T \][/tex]
(b) The rate of compound depreciation ([tex]\( R \)[/tex]) is:
[tex]\[ 8\% \][/tex]
(c) The initial cost of the mobile set ([tex]\( P \)[/tex]) is:
[tex]\[ \text{Rs.} 20,000 \][/tex]
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