A car whose cost is Rs. 9,00,000 will depreciate to a scrap value of…

The correct answer is Option (2) → (A), (B), and (D) only

Under the straight line method (the method used when none is named) the car loses the same amount every year:

    \( \displaystyle \text{Annual depreciation}=\frac{\text{Cost}-\text{Scrap value}}{\text{Useful life}} \)

    \( \displaystyle =\frac{9{,}00{,}000-1{,}20{,}000}{12} \)

    \( \displaystyle =\frac{7{,}80{,}000}{12} \)

    \( \displaystyle =65{,}000 \)

The book value at the end of year n is 9,00,000 − 65,000n:

    \( \displaystyle \text{Year 4: }9{,}00{,}000-2{,}60{,}000=6{,}40{,}000 \)

    \( \displaystyle \text{Year 5: }9{,}00{,}000-3{,}25{,}000=5{,}75{,}000 \)

    \( \displaystyle \text{Year 6: }9{,}00{,}000-3{,}90{,}000=5{,}10{,}000 \)

So the annual depreciation is Rs. 65,000, and the book value is Rs. 6,40,000 after 4 years, Rs. 5,75,000 after 5 years and Rs. 5,10,000 after 6 years.

Checking the statements

(A) The annual depreciation is Rs. 65,000 — Correct. \( \frac{7{,}80{,}000}{12}=65{,}000 \).

(B) The book value of the car at the end of the fourth year is Rs. 6,40,000 — Correct. 9,00,000 − 4 × 65,000 = 6,40,000.

(C) The book value of the car at the end of the sixth year is Rs. 5,00,000 — Incorrect. It is 9,00,000 − 6 × 65,000 = Rs. 5,10,000.

(D) The book value of the car at the end of the fifth year is Rs. 5,75,000 — Correct. 9,00,000 − 5 × 65,000 = 5,75,000.

CBSE Applied Mathematics (Class XII):
Depreciation