Certainly! Let's solve each part of the question step-by-step:
### a. Formula to Calculate Price After Increment
The formula to calculate the price of the machine after an increment of [tex]\( x \% \)[/tex] is given by:
[tex]\[ \text{Price after increment} = \text{Initial Price} \times \left(1 + \frac{x}{100}\right) \][/tex]
where [tex]\( x \)[/tex] is the percentage increase.
### b. Price of the Machine at the End of the First Year
Given:
- Initial price = Rs 16,00,000
- Increase in price in the first year = 10%
Using the formula from part (a):
[tex]\[ \text{Price after first year} = 1600000 \times \left(1 + \frac{10}{100}\right) \][/tex]
[tex]\[ \text{Price after first year} = 1600000 \times 1.10 \][/tex]
[tex]\[ \text{Price after first year} = 1760000 \][/tex]
So, the price of the machine at the end of the first year is Rs 17,60,000.
### c. Price of the Machine at the End of the Second Year
Given:
- Price after the first year = Rs 17,60,000
- Depreciation in the second year = 5%
The formula to calculate the price after depreciation is:
[tex]\[ \text{Price after depreciation} = \text{Price before depreciation} \times \left(1 - \frac{y}{100}\right) \][/tex]
where [tex]\( y \)[/tex] is the percentage depreciation.
Using the formula:
[tex]\[ \text{Price after second year} = 1760000 \times \left(1 - \frac{5}{100}\right) \][/tex]
[tex]\[ \text{Price after second year} = 1760000 \times 0.95 \][/tex]
[tex]\[ \text{Price after second year} = 1672000 \][/tex]
So, the price of the machine at the end of the second year is Rs 16,72,000.
### d. Price of the Machine at the End of the Third Year & Profit or Loss
Given:
- Price after the second year = Rs 16,72,000
- Depreciation in the third year = 4%
Using the depreciation formula again:
[tex]\[ \text{Price after third year} = 1672000 \times \left(1 - \frac{4}{100}\right) \][/tex]
[tex]\[ \text{Price after third year} = 1672000 \times 0.96 \][/tex]
[tex]\[ \text{Price after third year} = 1605120 \][/tex]
Now, to calculate profit or loss:
[tex]\[ \text{Profit/Loss} = \text{Selling Price} - \text{Initial Price} \][/tex]
[tex]\[ \text{Profit/Loss} = 1605120 - 1600000 \][/tex]
[tex]\[ \text{Profit/Loss} = 5120 \][/tex]
So, the machine is sold at a profit of Rs 5,120 at the end of the third year.
To summarize:
- The price of the machine at the end of the first year is Rs 17,60,000.
- The price of the machine at the end of the second year is Rs 16,72,000.
- The price of the machine at the end of the third year is Rs 16,05,120.
- The profit, if the machine is sold at the end of the third year, is Rs 5,120.
