The question is asking for the time it takes for a machine, originally worth Rs. 4,90,740, to depreciate to a value of Rs. 2,00,000. The depreciation rate is 15% per year on the opening value.

Here's how to solve it:

Step 1: Understand the problem
The machine is depreciating at a rate of 15% per year. This means that each year, the machine's value is 85% (100% - 15%) of its value at the start of that year.

Step 2: Set up the equation
We can express the value of the machine after n years as follows:
Value = Initial Value * (0.85)^n

Step 3: Substitute the given values
We know the initial value is Rs. 4,90,740 and the final value is Rs. 2,00,000. So we can set up the equation as follows:
2,00,000 = 4,90,740 * (0.85)^n

Step 4: Solve for n
Divide both sides by 4,90,740 to isolate the term with n:
(2,00,000 / 4,90,740) = (0.85)^n

Take the natural logarithm (ln) of both sides to get rid of the exponent:
ln(2,00,000 / 4,90,740) = n * ln(0.85)

Finally, solve for n by dividing both sides by ln(0.85):
n = ln(2,00,000 / 4,90,740) / ln(0.85)

Step 5: Calculate the value of n
When you calculate the above expression, you get n ≈ 4.6 years.

So, the closest answer is (a) 4 years 6 months.

Question

The question is asking for the time it takes for a machine, originally worth Rs. 4,90,740, to depreciate to a value of Rs. 2,00,000. The depreciation rate is 15% per year on the opening value.

Here's how to solve it:

Step 1: Understand the problem
The machine is depreciating at a rate of 15% per year. This means that each year, the machine's value is 85% (100% - 15%) of its value at the start of that year.

Step 2: Set up the equation
We can express the value of the machine after n years as follows:
Value = Initial Value * (0.85)^n

Step 3: Substitute the given values
We know the initial value is Rs. 4,90,740 and the final value is Rs. 2,00,000. So we can set up the equation as follows:
2,00,000 = 4,90,740 * (0.85)^n

Step 4: Solve for n
Divide both sides by 4,90,740 to isolate the term with n:
(2,00,000 / 4,90,740) = (0.85)^n

Take the natural logarithm (ln) of both sides to get rid of the exponent:
ln(2,00,000 / 4,90,740) = n * ln(0.85)

Finally, solve for n by dividing both sides by ln(0.85):
n = ln(2,00,000 / 4,90,740) / ln(0.85)

Step 5: Calculate the value of n
When you calculate the above expression, you get n ≈ 4.6 years.

So, the closest answer is (a) 4 years 6 months.

Knowee AI · Accepted Answer

The question is asking for the time it takes for a machine, originally worth Rs. 4,90,740, to depreciate to a value of Rs. 2,00,000. The depreciation rate is 15% per year on the opening value.

Here's how to solve it:

Step 1: Understand the problem
The machine is depreciating at a rate of 15% per year. This means that each year, the machine's value is 85% (100% - 15%) of its value at the start of that year.

Step 2: Set up the equation
We can express the value of the machine after n years as follows:
Value = Initial Value * (0.85)^n

Step 3: Substitute the given values
We know the initial value is Rs. 4,90,740 and the final value is Rs. 2,00,000. So we can set up the equation as follows:
2,00,000 = 4,90,740 * (0.85)^n

Step 4: Solve for n
Divide both sides by 4,90,740 to isolate the term with n:
(2,00,000 / 4,90,740) = (0.85)^n

Take the natural logarithm (ln) of both sides to get rid of the exponent:
ln(2,00,000 / 4,90,740) = n * ln(0.85)

Finally, solve for n by dividing both sides by ln(0.85):
n = ln(2,00,000 / 4,90,740) / ln(0.85)

Step 5: Calculate the value of n
When you calculate the above expression, you get n ≈ 4.6 years.

So, the closest answer is (a) 4 years 6 months.

A machine worth of Rs. 4,90,740 is depreciated at 15% on its opening valueeach year. When its value reduces to Rs. 2,00,000(a) 4 years 6 months(b) 4 years 7 months(c) 4 years 5 months(d) 5 years 7 months approximately

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