Sanjay purchased a hotel worth ₹ 10 lakh and barkha purchased a car worth ₹ 16 lakh. The value of hotel every year increases by `20%` of the previous value and the value of car every year depreciates by `25%`. What is the difference between the price of hotel and car after 3 years?

Options

A. ₹ 925000
B. ₹ 1053000
C. remains constant
D. can't be determined

Answer

To solve the problem step by step, we will calculate the value of the hotel and the car after 3 years and then find the difference between their values.

### Step 1: Calculate the value of the hotel after 3 years
- Initial value of the hotel = ₹10,00,000
- The hotel increases in value by 20% each year.

**Year 1:**
Value after 1 year = Initial value + (20% of Initial value)
= ₹10,00,000 + (20/100 * ₹10,00,000)
= ₹10,00,000 + ₹2,00,000
= ₹12,00,000

**Year 2:**
Value after 2 years = Value after 1 year + (20% of Value after 1 year)
= ₹12,00,000 + (20/100 * ₹12,00,000)
= ₹12,00,000 + ₹2,40,000
= ₹14,40,000

**Year 3:**
Value after 3 years = Value after 2 years + (20% of Value after 2 years)
= ₹14,40,000 + (20/100 * ₹14,40,000)
= ₹14,40,000 + ₹2,88,000
= ₹17,28,000

### Step 2: Calculate the value of the car after 3 years
- Initial value of the car = ₹16,00,000
- The car depreciates in value by 25% each year.

**Year 1:**
Value after 1 year = Initial value - (25% of Initial value)
= ₹16,00,000 - (25/100 * ₹16,00,000)
= ₹16,00,000 - ₹4,00,000
= ₹12,00,000

**Year 2:**
Value after 2 years = Value after 1 year - (25% of Value after 1 year)
= ₹12,00,000 - (25/100 * ₹12,00,000)
= ₹12,00,000 - ₹3,00,000
= ₹9,00,000

**Year 3:**
Value after 3 years = Value after 2 years - (25% of Value after 2 years)
= ₹9,00,000 - (25/100 * ₹9,00,000)
= ₹9,00,000 - ₹2,25,000
= ₹6,75,000

### Step 3: Find the difference between the values of the hotel and the car after 3 years
- Value of the hotel after 3 years = ₹17,28,000
- Value of the car after 3 years = ₹6,75,000

Difference = Value of the hotel - Value of the car
= ₹17,28,000 - ₹6,75,000
= ₹10,53,000

### Final Answer:
The difference between the price of the hotel and the car after 3 years is **₹10,53,000**.

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