# Solve the following : A factory building is insured for (56)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 - Mathematics and Statistics

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Sum

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.

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#### 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.

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Chapter 2: Insurance and Annuity - Miscellaneous Exercise 2 [Page 30]

#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 2 Insurance and Annuity
Miscellaneous Exercise 2 | Q 4.03 | Page 30
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