Question

A bike costing ₹120000 has a scrap value of ₹30000. If the book value of the bike at the end of third year is ₹90000, then the useful life of the bike is,

• A. 6 years
• B. 12 years
• C. 10 years
• D. 9 years

Answer 1

The Correct Option is D

To determine the useful life of the bike, we use the Straight-Line Depreciation method where the depreciation amount per year is constant. Let's calculate the depreciation using the given values:

1. Cost of the bike: ₹120,000
2. Scrap value (residual value): ₹30,000
3. Book value at end of Year 3: ₹90,000

Let's denote the following:

• C = Initial cost of the bike = ₹120,000
• S = Scrap value = ₹30,000
• V₃ = Book value at end of Year 3 = ₹90,000
• D = Annual Depreciation
• n = Useful life of the bike (in years)

Using the straight-line depreciation formula:

D = \(\frac{C-S}{n}\)

The depreciation after 3 years is:

D × 3 = C - V₃

Substitute the values:

D × 3 = 120,000 - 90,000

Calculate the total depreciation over 3 years:

D × 3 = 30,000

Solve for annual depreciation:

D = \(\frac{30,000}{3}\) = 10,000

Now find n using:

D = \(\frac{120,000-30,000}{n}\)

10,000 = \(\frac{90,000}{n}\)

Solving for n:

n = \(\frac{90,000}{10,000}\) = 9

Therefore, the useful life of the bike is 9 years.

The correct answer is:

• 9 years