Question

Assertion: A machine costing ₹ 50,000 depreciates by 10% every year then its value after 2 years is ₹ 40,500.

Reason: When ₹ 40,500 increases by 10% its value after 2 years will be ₹ 50,000.

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

A is true but R is false.

Explanation:

Given:

• Cost of machine P = ₹ 50,000 
• Depreciation = 10% per year
• Time = 2 years
• Find the value after 2 years

The assertion: Value after 2 years = ₹ 40,500

The reason: If ₹ 40,500 increases by 10%, its value after 2 years will be ₹ 50,000

Step 1: Calculate the value after 2 years (depreciation)

Depreciation formula:

`V = P(1 - r/100)^n`

Substitute the values:

`V = 50,000(1 - 10/100)^2`

`V = 50,000 xx (0.9)^2`

`V = 50,000 xx 0.81`

V = 40,500

Assertion is true.

Step 2: Check the reason

• Reason: “When ₹ 40,500 increases by 10%, its value after 2 years will be ₹ 50,000”
• Let’s check: 40,500 × (1 + 0.10)²
  = 40,500 × (1.1)²
  = 40,500 × 1.21
  = 48,405
• This is not ₹ 50,000

Reason is false.