Question 171 markMCQSection A

A machine costs Rs 45,000 with an estimated useful life of 5 years and a scrap value of Rs 10,000. The annual depreciation of the machine is :

Financial Mathematics
Depreciation (Straight Line Method)

Options

(A)Rs 8,000
(B)Rs 7,000
(C)Rs 6,000
(D)Rs 5,000

Official answer

The correct option is (B) Rs 7,000.


Formula (Straight Line Method):

  • Annual Depreciation = (Cost−Scrap Value)÷Useful Life(\text{Cost} - \text{Scrap Value}) \div \text{Useful Life}

Substitution:

  • = (45,000−10,000)÷5(45,000 - 10,000) \div 5
  • = 35,000÷535,000 \div 5 = Rs 7,000 per year
Answer keywords:straight line methodannual depreciationscrap valuesalvage valueuseful lifedepreciable amountcost of asset

Marking scheme

  1. 1.1 mark: correct option (B) Rs 7,000 with the SLM formula (Cost−Scrap)/Life(\text{Cost} - \text{Scrap})/\text{Life} applied.
  2. 2.Accept a clearly shown computation (45000−10000)/5=7000(45000 - 10000)/5 = 7000 even if the letter is not circled.

Hint

Depreciable amount = Cost−Scrap value\text{Cost} - \text{Scrap value}; then divide by useful life.

Quick oral answer

By the straight line method, annual depreciation equals cost minus scrap value divided by useful life, which is (45,000 minus 10,000) over 5, giving Rs 7,000 every year.

Common mistakes

  1. 1.Dividing the full cost (45,000) by 5 and forgetting to subtract the scrap value of Rs 10,000.
  2. 2.Confusing Straight Line Method with Written Down Value (WDV) method, which uses a fixed percentage on the reducing book value.
  3. 3.Adding the scrap value to the cost instead of subtracting it from the cost.

Analysis and explanation

This question tests the Straight Line Method (SLM) of depreciation, where an asset loses an equal amount of value every year over its useful life.


Why (B) is correct:

  • Total value lost over life = Cost−Scrap=45,000−10,000=35,000\text{Cost} - \text{Scrap} = 45,000 - 10,000 = 35,000.
  • Spread equally over 5 years: 35,000÷535,000 \div 5 = Rs 7,000 each year.

Why the distractors are wrong:

  • (A) Rs 8,000 — obtained by wrongly dividing only the cost 40,000/540,000/5 or mishandling scrap; ignores correct depreciable base.
  • (C) Rs 6,000 — results from taking 30,000/530,000/5, i.e. subtracting a wrong scrap value.
  • (D) Rs 5,000 — results from dividing 45,000 − 10,000 by 7, or dividing 25,000/525,000/5; a miscalculation of the base.

Exam trap: Never divide the full cost by life. Always subtract the scrap (salvage) value first to get the depreciable amount.

Interesting facts

The Straight Line Method is the most widely used depreciation method in Indian company accounts because it is simple and produces a constant annual expense, aiding budgeting.

Under the Companies Act, 2013, depreciation is charged based on the useful life of an asset (Schedule II) rather than fixed rates, making the (Cost−Scrap)/Life(\text{Cost} - \text{Scrap})/\text{Life} idea legally central.

Question details

Q17 of 44 questions

Board
CBSE
Class
Class 12
Subject
Applied Mathematics
Year
2026
Section
Section A
Marks
1
Type
MCQ
Chapter
Financial Mathematics
Topic
Depreciation (Straight Line Method)
Bloom's level
apply
Syllabus topic
Unit: Financial Mathematics — Depreciation using the Straight Line (Linear) Method
Author
CBSE
Reviewed by
Padhantu Academic Team

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Frequently asked questions

What is the difference between the Straight Line Method and the Written Down Value Method?

In the Straight Line Method, a constant amount is depreciated every year, computed as (Cost−Scrap)/Life(\text{Cost} - \text{Scrap})/\text{Life}. In the Written Down Value (Reducing Balance) Method, a fixed percentage is applied each year to the reducing book value, so the depreciation amount is largest in the first year and decreases every subsequent year.

Why is scrap value subtracted before computing depreciation?

Scrap (or salvage) value is the amount expected to be recovered when the asset is sold at the end of its useful life. Since that portion of value is not lost, only the difference (Cost−Scrap)(\text{Cost} - \text{Scrap}) is the depreciable amount that is written off over the life of the asset.