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Question
Solve the following :
A cargo of grain is insured at `(3/4)`% to cover 70% of its value. ₹1,008 is the amount of premium paid. If the grain is worth ₹12 per kg, how many kg of the grain did the cargo contain?
Solution
Let the property value of cargo be ₹ x.
Since, cargo is insured to 70% of its value,
∴ Policy value = 70% of property value
= `(70)/(100) xx x`
= `₹ (7x)/(10)`
Rate of perimum = `(3)/(4)`%
Amount of perimum = ₹1.008.
∴ Amount od premium = `(3)/(4)`% of policy value
∴ 1,008 = `(3)/(4) xx (1)/(100) xx (7x)/(10)`
∴ x = `(1008 xx 4 xx 100 x 10)/(3 xx 7)`
∴ x = ₹1,,92,000
∴ Property value of cargo is ₹,92,000,
i.e., cargo contains grain of ₹1,92,000.
Price of grain is ₹12 per kg.
∴ Capacity of cargo = `"Value of cargo"/"Price of 1kg grain"`
= `(192,000)/(12)`
= 16,000 kgs
∴ Cargo contains 16,000 kgs of grains.
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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`
Annualized average rate per bonus = ₹ 20 per thousand per year
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`
