Maharashtra Board Class 12 Maths Part 2 Chapter 2 Insurance and Annuity 2.1 Solutions

Question 1. Find the premium on a property worth Rs. 25,00,000 at 3% if
(i) the property is fully insured
(ii) the property is insured for 80% of its value.
Answer:
Solution:
Case-1
Property value = Rs. 25,00,000
Rate of Premium = 3%
Policy Value = Rs. 25,00,000
∴ Amount of Premium = 3% \( \times \) 25,00,000 = Rs. 75,000
Case-2
Property Value = Rs. 25,00,000
Policy value = 80% \( \times \) 25,00,000 = Rs. 20,00,000
Rate of Premium = 3%
∴ Amount of Premium = 3% \( \times \) 20,00,000 = Rs. 60,000
In simple words: This problem calculates the insurance premium for a property under two scenarios: full insurance and 80% insurance, using the given property value and premium rate. It demonstrates how the policy value affects the total premium.

🎯 Exam Tip: Remember to calculate the "Policy Value" first, especially if the property is not fully insured, as the premium is always based on the insured amount.

Question 2. A shop is valued at Rs. 3,60,000 for 75% of its value. If the rate of premium is 0.9%, find the premium paid by the owner of the shop. Also, find the agents commission if the agent gets commission at 15% of the premium.
Answer:
Solution:
Property Value = Rs. 3,60,000
Policy Value = 75% \( \times \) 3,60,000 = Rs. 2,70,000
Rate of Premium = 0.9%
∴ Amount of Premium = 0.9% \( \times \) 2,70,000 = Rs. 2,430
Rate of Commission = 15%
∴ Amount of Commission = 15% \( \times \) 2,430 = Rs. 364.5
In simple words: This solution calculates the insurance premium based on a percentage of the shop's value and then determines the agent's commission as a percentage of that premium. It shows the total cost for the owner including the agent's fee.

🎯 Exam Tip: Pay close attention to whether the premium rate is applied to the full property value or a percentage of it (policy value). Also, ensure commission is calculated on the premium amount.

Question 3. A person insures his office valued at Rs. 5,00,000 for 80% of its value. Find the rate of premium if he pays Rs. 13,000 as premium. Also, find agent's commission at 11%.
Answer:
Solution:
Property Value = Rs. 5,00,000
Policy Value = 80% \( \times \) 5,00,000 = Rs. 4,00,000
Amount of Premium = Rs. 13000
Let the rate of Premium be \(x\)%
Amount of premium = Rate \( \times \) Policy Value
∴ 13000 = \(x\)% \( \times \) 4,00,000
\( \implies \) \( \frac{13,000}{4,00,000} = \frac{x}{100} \)
\( \implies \) \( \frac{13,000 \times 100}{4,00,000} = x \)
\( \implies \) \(x\) = 3.25%
Rate of commission = 11%
∴ Amount of Commission = 11% \( \times \) 13,000 = Rs. 1,430
In simple words: This problem involves calculating the percentage rate of premium when the property value, policy value, and premium amount are known. It then proceeds to calculate the agent's commission based on this premium.

🎯 Exam Tip: When finding the rate of premium, ensure to set up the equation correctly relating premium amount, policy value, and the unknown rate. Always calculate commission on the premium.

Question 4. A building is insured for 75% of its value. The annual premium at 0.70 percent amounts to Rs. 2625. If the building is damaged to the extent of 60% due to fire, how much can be claimed under the policy?
Answer:
Solution:
Let the Property Value of building be \(x\)
Policy Value = 75% \( \times \) \(x\) = 0.75\(x\)
Rate of Premium = 0.70%
Amount of Policy = Rate \( \times \) Policy Value
2625 = 0.70% \( \times \) 0.75\(x\)
2625 = \( \frac{0.70}{100} \times 0.75x \)
\( \implies \) \( \frac{2625}{0.75} = \frac{0.70}{100} \times x \)
\( \implies \) \( 3500 = \frac{0.70}{100} \times x \)
\( \implies \) \( \frac{3500 \times 100}{0.70} = x \)
\( \implies \) \(x\) = 5,00,000
∴ Damage = 60% \( \times \) Property Value
= \( \frac{60}{100} \times 5,00,000 \)
= Rs. 3,00,000
∴ Policy Value (of damaged amount) = 0.75 \( \times \) 3,00,000 = Rs. 2,25,000
∴ Claim = \( \frac{\text{Policy value}}{\text{Property value}} \times \text{Loss} \)
= \( \frac{2,25,000}{5,00,000} \times 3,00,000 \)
= Rs. 1,35,000
In simple words: This problem first determines the total property value using the premium paid and the insurance rate. Then, given the extent of damage, it calculates the actual loss and the final claim amount based on the proportion of the property insured.

🎯 Exam Tip: It is crucial to distinguish between the full property value and the insured (policy) value when calculating both premium and claim amount. The claim is always limited by the policy value and the actual loss, whichever is lower.

Question 5. A stock worth Rs. 7,00,000 was insured for Rs. 4,50,000. Fire burnt stock worth Rs. 3,00,000 completely and damaged there remaining stock to the extent of 75% of its value. What amount can be claimed undertaken policy?
Answer:
Solution:
Property Value = Rs. 7,00,000
Policy Value = Rs. 4,50,000
Complete Loss = 3,00,000
Partial loss = 75% \( \times \) [7,00,000 – 3,00,000]
= \( \frac{75}{100} \times 4,00,000 \)
= Rs. 3,00,000
∴ Total loss = Rs. 3,00,000 + Rs. 3,00,000 = Rs. 6,00,000
∴ Claim = \( \frac{\text{Policy value}}{\text{Property value}} \times \text{Loss} \)
= \( \frac{4,50,000}{7,00,000} \times 6,00,000 \)
= Rs. 3,85,714.29
In simple words: This problem involves calculating the total loss for a partially insured stock, differentiating between complete loss and partial damage, and then determining the claimable amount using the policy value and total property value.

🎯 Exam Tip: When calculating loss, distinguish between completely destroyed stock and partially damaged stock. The claim amount is prorated based on the ratio of policy value to property value.

Question 6. A cargo of rice was insured at 0.625 % to cover 80% of its value. The premium paid was Rs. 5,250. If the price of rice is Rs. 21 per kg. find the quantity of rice (in kg) in the cargo.
Answer:
Solution:
Let Property Value be \(x\)
Policy Value = 80% \( \times \) \(x\) = Rs. 0.8\(x\)
Rate of Policy = 0.625%
Amount of Premium = Rate \( \times \) Policy value
∴ 5250 = 0.625% \( \times \) 0.8\(x\)
∴ 5250 = 0.005\(x\)
\( \implies \) \( x = \frac{5250}{0.005} \)
∴ \(x\) = Rs. 10,50,000
Rate of Rice = 21/kg
∴ Quantity of Rice (in kg) = \( \frac{\text{Total value}}{\text{Rate of Rice}} \)
= \( \frac{10,50,000}{21} \)
= 50,000 kgs
In simple words: This solution determines the total value of the rice cargo by using the premium paid and the insurance rate. Then, it calculates the quantity of rice in kilograms by dividing the total value by the price per kilogram.

🎯 Exam Tip: This problem combines insurance calculations with unit cost calculations. Ensure to first find the total value of the cargo using the premium details, then apply the per-unit cost to find the quantity.

Question 7. 60,000 articles costing Rs. 200 per dozen were insured against fire for Rs. 2,40,000. If 20% of the articles were burnt and 7,200 of the remaining articles were damaged to the extent of 80% of their value, find the amount that can be claimed under the policy.
Answer:
Solution:
No of articles = 60,000
Cost of articles = Rs. 200/dozen
∴ Property of Value = \( \frac{60,000}{12} \times 200 = \text{Rs. } 10,00,000 \)
∴ Policy Value = Rs. 2,40,000
Complete Loss = 20% \( \times \) 10,00,000 = Rs. 2,00,000
Partial loss = \( \frac{7200}{12} \times 200 \times 80\% = \text{Rs. } 96,000 \)
∴ Total loss = 2,00,000 + 96,000 = Rs. 2,96,000
Claim = \( \frac{\text{Policy value}}{\text{Property value}} \times \text{Loss} \)
= \( \frac{2,40,000}{10,00,000} \times 2,96,000 \)
= Rs. 71,040
In simple words: This problem calculates the total property value based on the number of articles and their cost per dozen. It then determines the total loss from both completely burnt and partially damaged articles, and finally computes the claimable amount using the policy and property values.

🎯 Exam Tip: Accurately calculate the total property value from per-dozen cost and then meticulously sum up the complete and partial losses before applying the prorata claim formula.

Question 8. The rate of premium is 2% and other expenses are 0.075%. A cargo worth Rs. 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.
Answer:
Solution:
Let the Policy Value of Cargo be Rs. 100 which includes insurance and other expenses
∴ Property Value = 100 - [2 + 0.075] = Rs. 97.925
If Policy Value is Rs. 100, then Property Value is 97.925
If Property Value is Rs. 3,50,100
Then policy Value = \( \frac{100 \times 3,50,100}{97.925} = \text{Rs. } 3,57,518.51 \)
In simple words: This problem involves calculating the required policy value for a cargo so that its original worth, along with the insurance premium and other expenses, can be fully recovered in case of total loss. It uses a proportional method to find the true policy value.

🎯 Exam Tip: This question requires a unique approach where the policy value covers itself plus the property. Set up a base case (e.g., Rs. 100 policy value) to determine the effective property value and then scale it.

Question 9. A property worth Rs. 4,00,000 is insured with three companies. A, B, and C. The amounts insured with these companies are Rs. 1,60,000, Rs. 1,00,000 and Rs. 1,40,000 respectively. Find the amount recoverable from each company in the event of a loss to the extent of Rs. 9,000.
Answer:
Solution:
Property Value = Rs. 4,00,000
Loss = Rs. 9,000
Total Value of Policies = 1,60,000 + 1,00,000 + 1,40,000 = Rs. 4,00,000
Claim = \( \frac{\text{Policy value}}{\text{Property value}} \times \text{Loss} \)
Claim of company A = \( \frac{1,60,000}{4,00,000} \times 9,000 = \text{Rs. } 3,600 \)
Claim of company B = \( \frac{1,00,000}{4,00,000} \times 9,000 = \text{Rs. } 2,250 \)
Claim of company C = \( \frac{1,40,000}{4,00,000} \times 9,000 = \text{Rs. } 3,150 \)
In simple words: This problem calculates the individual claim amounts from three different insurance companies that collectively insured a property. Each company pays a proportionate share of the total loss based on its individual policy value relative to the total insured amount.

🎯 Exam Tip: When multiple policies cover a single property, the total loss is distributed among the insurers proportionally to their respective policy values against the total insured value.

Question 10. A car valued at Rs. 8,00,000 is insured for Rs. 5,00,000. The rate of premium is 5% less 20%. How much will the owner bear including the premium if value of the ear is reduced to 60% of its original value.
Answer:
Solution:
Property Value = Rs. 8,00,000
Policy Value = Rs. 5,00,000
Rate of Premium = 5% less 20%
= 5% - 20% \( \times \) 5%
= (5 - 1)%
= 4%
Amount of Premium = 4% \( \times \) 5,00,000 = Rs. 20,000
Loss = [100 - 60]% \( \times \) Property Value
= 40% \( \times \) 8,00,000
= Rs. 3,20,000
Claim = \( \frac{\text{Policy value}}{\text{Property value}} \times \text{Loss} \)
= \( \frac{5,00,000}{8,00,000} \times 3,20,000 \)
= Rs. 2,00,000
Loss bear by owner = Loss - claim + Premium
= 3,20,000 - 2,00,000 + 20,000
= Rs. 1,40,000
In simple words: This problem determines the actual premium paid after a discount, calculates the total loss due to reduced car value, and then finds the insurance claim. Finally, it calculates the net amount the owner has to bear, considering the premium paid and the difference between total loss and the claim received.

🎯 Exam Tip: Carefully calculate the effective premium rate after any discounts. The amount borne by the owner is the total loss minus the claim received, plus the premium paid.

Question 11. A shop and a godown worth Rs. 1,00,000 and Rs. 2,00,000 respectively were insured through an agent who was paid 12% of the total premium. If the shop was insured for 80% and the godown for 60% of their respective values, find the agent's commission, given that the rate of premium was 0.80% less 20%.
Answer:
Solution:
Rate of Premium = 0.80% Less 20%
= 0.80% - 20% \( \times \) 0.80%
= (0.80 - 0.16)%
= 0.64%
For Shop
Property Value = Rs. 1,00,000
Policy Value = 80% \( \times \) 1,00,000 = Rs. 80,000
Premium = 0.64% \( \times \) 80,000 = Rs. 512
For Godown
Property Value = Rs. 2,00,000
Policy Value = 60% \( \times \) 2,00,000 = Rs. 1,20,000
Premium = 0.64% \( \times \) 1,20,000 = Rs. 768
∴ Total Premium = 512 + 768 = Rs. 1,280
Rate of Commission = 12%
∴ Agent Commission = 12% \( \times \) 1,280 = Rs. 153.6
In simple words: This solution first calculates the effective premium rate after a discount. Then, it determines the individual policy values and premiums for both a shop and a godown. Finally, it calculates the agent's commission based on the combined total premium.

🎯 Exam Tip: Ensure to calculate the effective premium rate correctly after any reductions. Treat each insured property separately for premium calculation, then sum them up for total premium before calculating agent's commission.

Question 12. The rate of premium on a policy of Rs. 1,00,000 is Rs. 56 per thousand per annum. A rebate of 0.75 per thousand is permitted if the premium is paid annually. Find the net amount of premium payable if the policy holder pays the premium annually.
Answer:
Solution:
Policy Value = Rs. 1,00,000
Rate of Premium = 56 per thousand p.a
Rate of Rebate = 0.75 per thousand p.a
Premium is paid annually
∴ Net rate of = 56 – 0.75 = Rs. 55.25 per thousand p.a.
∴ Net Amount ot Premium = \( \frac{1,00,000}{1000} \times 55.25 = \text{Rs. } 5,525 \)
In simple words: This problem calculates the net premium payable for an insurance policy by first subtracting a per-thousand rebate from the original premium rate and then applying this adjusted rate to the total policy value.

🎯 Exam Tip: When given a premium rate 'per thousand', divide the policy value by 1000 before multiplying by the rate. Ensure to correctly apply any rebates to the rate first.

Question 13. A warehouse valued at Rs. 40,000 contains goods worth Rs. 2,40,000. The warehouse is insured against fire for Rs. 16,000 and the goods to the extent of 90% of their value. Goods worth Rs. 80,000 are completely destroyed, while the remaining goods are destroyed to 80% of their value due to a fire. The damage to the warehouse is to the extent of Rs. 8,000. Find the total amount that can be claimed.
Answer:
Solution:
For Warehouse
Property Value = Rs. 40,000
Policy Value = Rs. 16,000
Loss = Rs. 8,000
Claim = \( \frac{\text{Policy value}}{\text{Property value}} \times \text{Loss} \)
= \( \frac{16,000}{40,000} \times 8,000 \)
= Rs. 3,200
For Goods
Property Value = Rs. 2,40,000
Policy Value = 90% \( \times \) 2,40,000 = Rs. 2,16,000
Complete Loss = 80,000
Partial Loss = 80% \( \times \) (2,16,000 - 80,000)
= 80% \( \times \) 1,36,000
= Rs. 1,08,800
Claim = \( \frac{\text{Policy value}}{\text{Property value}} \times \text{Loss} \)
= \( \frac{2,16,000}{24,000} \times 1,08,800 \)
= Rs. 97,920
∴ Total Claim = 3,200 + 97,920 = Rs. 1,01,120
In simple words: This complex problem calculates the claimable amount separately for a warehouse and its goods, considering their individual property and policy values, as well as distinct complete and partial losses. The total claim is the sum of claims from both categories.

🎯 Exam Tip: This question involves multiple insurance calculations (warehouse and goods) and different types of losses (complete and partial). It's essential to calculate each component meticulously and sum them up for the final answer. Double-check the policy value used for goods, which is 90% of their value in this case.

Question 14. A person takes a life policy for Rs. 2,00,000 for a period of 20 years. He pays premium for 10 years during which bonus was declared at an average rate of Rs. 20 per year per thousand. Find the paid up value of the policy if he discontinuous paying premium after 10 years.
Answer:
Solution:
Policy Value = Rs. 2,00,000
Rate of Bonus = Rs. 20 Per thousand p.a.
Total Bonus = \( \frac{2,00,000 \times 20}{1,000} = \text{Rs. } 4,000 \)
∴ Bonus for 10 years = 4,000 \( \times \) 10 = Rs. 40,000
Period of Policy = 20 years
∴ Amount of Premium = \( \frac{2,00,000}{20} = \text{Rs. } 10,000 \text{ p.a.} \)
∴ Total Premium for 10 years = 10,000 \( \times \) 10 = Rs. 1,00,000
∴ Paid up Value of Policy = Total premium + Total Bonus
= 1,00,000 + 40,000
= Rs. 1,40,000
In simple words: This problem calculates the paid-up value of a life insurance policy when premiums are discontinued after a certain period. It involves summing the total premiums paid and the accumulated bonus over the period of payment to determine the policy's final worth.

🎯 Exam Tip: For paid-up value, ensure to calculate the total bonus accumulated over the premium paying period, not the full policy term, and then add it to the total premium actually paid.