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The rate of premium is 2% and other expenses are 0.75%. A cargo worth ₹ 3,50,100 is to be insured so that all its value and the cost of insurance will be recovered in the event of total loss.

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#### Solution

Property value = 3,50,100

Let insured value = a.

∴ premium = `(2"a")/100`

Other expenses = 0.75% of a

`= (75 "a")/(10,000)`

∴ Insured value = Property value + Premium + Other expenses

∴ a = 3,50,100 + `(2"a")/100 + (75 "a")/(10,000)`

∴ a = 3,50,100 + `(2"a" xx 100)/(100 xx 100) + (75 "a")/(10,000)` ....(Multiplied by 100)

∴ a = 3,50,100 + `(200"a")/10000 + (75 "a")/(10,000)`

∴ a = 3,50,100 + `(275 "a")/(10,000)`

∴ a - `(275 "a")/(10,000)` = 3,50,100

∴ `(10,000 "a" - 275 "a")/(10,000) = 3,50,100`

∴ `(9,725 "a")/(10,000)` = 3,50,100

∴ a = `3,50,100 xx (10,000)/(9,725)`

∴ a = 3,60,000

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Property value = ₹ 12,50,000

Rate of premium, r = ₹ 3%

If property is fully insured, the policy value is same as property value therefore policy value = `square`

Premium = `"r"/100 xx "policy value"`

= `square/100 xx 12,50,000`

= `square`

Policy value = ₹ 80,000

Period of policy = 20 years

Amount of money paid in 10 years = `square`

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For one year, bonus = `square/1000 xx 80,000`

= ₹ 1,600

Bonus for 10 years = `10 xx square`

= ₹ 16,000

Total amount after 10 years = `square + 16000`

= ₹ `square`

Property value = ₹ 12,50,000

Rate of premium, r = ₹ 3%

If property is 80% insured

Policy value = 80% of its property value

= `square/100 xx 12,50,000`

= ₹ 10,00,000

Premium = `square/100 xx 10,00,000`

= ₹ `square`