A building of initial value Rs. 31,25,000 depreciates in its value every year at the rate of 4% on its value at the beginning of the year. If Rs. x is the value of the building at the end of 3 years and Rs. y is the value of the land which appreciates at the rate of 5% compoundingly and the value of the land initially is Rs 32,00,000 then y - x =

Given:

Initial value of building (P_building) = ₹31,25,000

Depreciation rate of building (r_building) = 4%

Time (t_building) = 3 years

Initial value of land (P_land) = ₹32,00,000

Appreciation rate of land (r_land) = 5%

Time (t_land) = 3 years

Formula used:

For depreciation: A = P × (1 - r/100)^t

For appreciation: A = P × (1 + r/100)^t

Calculations:

For building value after 3 years (x):

A_building = P_building × (1 - r_building/100)^t_building

⇒ A_building = 31,25,000 × (1 - 4/100)³

⇒ A_building = 31,25,000 × (0.96)³

⇒ A_building = ₹27,64,800

For land value after 3 years (y):

A_land = P_land × (1 + r_land/100)^t_land

⇒ A_land = 32,00,000 × (1 + 5/100)³

⇒ A_land = 32,00,000 × (1.05)³

⇒ A_land = ₹37,04,400

Difference (y - x):

y - x = A_land - A_building

⇒ y - x = 37,04,400 - 27,64,800 = ₹9,39,600

∴ The correct answer is option (2).