**Solve the following :**

A factory building is insured for `(5/6)^"th"` of its value at a rate of premium of 2.50%. If the agent is paid a commission of ₹2,812.50, which is 7.5% of the premium, find the value of the building.

#### Solution

Let the property value of the factory building be ₹ x.

Since, the building is insured for `(5/6)^"th"` of its value,

∴ Policy value = `(5/6)^"th"` of property value

= `(5)/(6) xx x`

= `(5x)/(6)`

Rate of perimum is 2.5%

∴ Amount of perimum = 2.50% of policy value

= `(2.50)/(100) xx (5x)/(6)`

= `(0.1)/(4) xx (5x)/(6x)`

= `(0.5x)/(24)`

Agent’s commission is ₹2,812.50 and his rate of commission is 7.5 % of premium.

Agent’s commission = 7.5 % of premium

∴ 2,812.50 = `(7.5)/(100) xx (0.5x)/(24)`

∴ 2,812.50 = `(0.3)/(4) xx (0.5x)/(24)`

∴ 2,812.50 = `(0.1)/(4) xx (0.5x)/(8)`

∴ 2,812.50 = `(0.05x)/(32)`

∴ x = `(2,812.50 xx 32)/(0.05)`

∴ x = 56,250 x 32

∴ x = ₹18,00,000

∴ Property value of the factory building is 18 lakh rupees.