A Rs. 2 lakh item attains its scrap value of Rs. 50,000 in 15 years. If linear depreciation is applicable, then which of the following statements are correct?
(A) The annual depreciation is Rs. 5,000.
(B) The annual depreciation is Rs. 10,000.
(C) Depreciation rate is 10 %.
(D) Depreciation rate is 6.67 %.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (B) and (D) only
In linear (straight-line) depreciation, the same amount is written off every year, so that the value falls from the cost C to the scrap value S in n years.
\( \displaystyle \text{Annual depreciation}=\frac{C-S}{n} \)
\( \displaystyle =\frac{200000-50000}{15} \)
\( \displaystyle =\frac{150000}{15} \)
\( \displaystyle =\text{Rs. }10000 \)
The rate of depreciation in the linear method is the fraction of the depreciable amount (C − S) written off each year:
\( \displaystyle \text{Rate}=\frac{10000}{150000}\times 100\% \)
\( \displaystyle =\frac{100}{15}\%=6.67\% \)
So the annual depreciation is Rs. 10,000 and the rate of depreciation is 6.67%.
Checking the statements
(A) The annual depreciation is Rs. 5,000. — Incorrect. It is Rs. 10,000.
(B) The annual depreciation is Rs. 10,000. — Correct. (2,00,000 − 50,000) ÷ 15 = 10,000.
(C) Depreciation rate is 10 %. — Incorrect. The rate is 6.67%.
(D) Depreciation rate is 6.67 %. — Correct. 10,000 out of 1,50,000 each year is 6.67%.