Balbharati Maharashtra State Board 12th Commerce Maths Digest Pdf Chapter 2 Insurance and Annuity Ex 2.1 Questions and Answers.

## Maharashtra State Board 12th Commerce Maths Solutions Chapter 2 Insurance and Annuity Ex 2.1

Question 1.

Find the premium on a property worth ₹ 25,00,000 at 3% if

(i) the property is fully insured

(ii) the property is insured for 80% of its value.

Solution:

Case-1

Property value = ₹ 25,00,000

Rate of Premium = 3%

Policy Value = ₹ 25,00,000

∴ Amount of Premium = 3% × 25,00,000 = ₹ 75,000

Case-2

Property Value = ₹ 25,00,000

Policy value = 80% × 25,00,000 = ₹ 20,00,000

Rate of Premium = 3%

∴ Amount of Premium = 3% × 20,00,000 = ₹ 60,000

Question 2.

A shop is valued at ₹ 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.

Solution:

Property Value = ₹ 3,60,000

Policy Value = 75% × 3,60,000 = ₹ 2,70,000

Rate of Premium = 0.9%

∴ Amount of Premium = 0.9% × 2,70,000 = ₹ 2,430

Rate of Commission = 15%

∴ Amount of Commission = 15% × 2,430 = ₹ 364.5

Question 3.

A person insures his office valued at ₹ 5,00,000 for 80% of its value. Find the rate of premium if he pays ₹ 13,000 as premium. Also, find agent’s commission at 11%.

Solution:

Property Value = ₹ 5,00,000

Policy Value = 80% × 5,00,000 = ₹ 4,00,000

Amount of Premium = ₹ 13000

Let the rate of Premium be x%

Amount of premium = Rate × Policy Value

∴ 13000 = x% × 4,00,000

∴ \(\frac{13,000}{4,00,000}=\frac{x}{100}\)

∴ \(\frac{13,000 \times 100}{4,00,000}\) = x

∴ x = 3.25%

Rate of commission = 11%

∴ Amount of Commission = 11% × 13,000 = ₹ 1,430

Question 4.

A building is insured for 75% of its value. The annual premium at 0.70 percent amounts to ₹ 2625. If the building is damaged to the extent of 60% due to fire, how much can be claimed under the policy?

Solution:

Let the Property Value of building be ₹ x

Policy Value = 75% × x = 0.75x

Rate of Premium = 0.70%

Amount of Policy = Rate × Policy Value

2625 = 0.70% × 0.75x

\(\frac{2625}{0.75}\) = 0.70% × x

3520 = \(\frac{0.70}{100}\) × x

\(\frac{3500 \times 100}{0.70}\) = x

x = ₹ 5,00,000

∴ Damage = 60% × Property Value

= \(\frac{60}{100}\) × 5,00,000

= ₹ 3,00,000

∴ Policy Value = 0.75 × 3,00,000 = ₹ 2,25,000

∴ Claim = \(\frac{\text { Policy value }}{\text { Property value }}\) × Loss

= \(\frac{2,25,000}{5,00,000}\) × 3,00,000

= ₹ 1,35,000

Question 5.

A stock worth ₹ 7,00,000 was insured for ₹ 4,50,000. Fire burnt stock worth ₹ 3,00,000 completely and damaged there remaining stock to the extent of 75% of its value. What amount can be claimed undertaken policy?

Solution:

Property Value = ₹ 7,00,000

Policy Value = ₹ 4,50,000

Complete Loss = 3,00,000

Partial loss = 75% × [7,00,000 – 3,00,000]

= \(\frac{75}{100}\) × 4,00,000

= ₹ 3,00,000

∴ Total loss = ₹ 3,00,000 + ₹ 3,00,000 = ₹ 6,00,000

∴ Claim = \(\frac{\text { Policy value }}{\text { Property value }}\) × Loss

= \(\frac{4,50,000}{7,00,000}\) × 6,00,000

= ₹ 3,85,714.29

Question 6.

A cargo of rice was insured at 0.625 % to cover 80% of its value. The premium paid was ₹ 5,250. If the price of rice is ₹ 21 per kg. find the quantity of rice (in kg) in the cargo.

Solution:

Let Property Value be ₹ x

Policy Value = 80% × x = ₹ 0.8x

Rate of Policy = 0.625%

Amount of Premium = Rate × Policy value

∴ 5250 = 0.625% × 0.8x

∴ 5250 = 0.005x

∴ x = \(\frac{5250}{0.005}\)

∴ x = ₹ 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

Question 7.

60,000 articles costing ₹ 200 per dozen were insured against fire for ₹ 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.

Solution:

No of articles = 60,000

Cost of articles = ₹ 200/dozen

∴ Property of Value = \(\frac{60,000}{12}\) × 200 = ₹ 1o,oo,ooo

∴ Policy Value = ₹ 2,40,000

Complete Loss = 20% × 10,00,000 = ₹ 2,00,000

Partial loss = \(\frac{7200}{12}\) × 200 × 80% = ₹ 96,000

∴ Total loss = 2,00,000 + 96,000 = ₹ 2,96,000

Claim = \(\frac{\text { Policy value }}{\text { Property value }}\) × Loss

= \(\frac{2,40,000}{10,00,000}\) × 2,96,000

= ₹ 71,040

Question 8.

The rate of premium is 2% and other expenses are 0.075%. 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.

Solution:

Let the Policy Value of Cargo be ₹ 100 which includes insurance and other expenses

∴ Property Value = 100 – [2 + 0.075] = ₹ 97.925

If Policy Value is ₹ 100, then Property Value is ₹ 97.925

If Property Value is ₹ 3,50,100

Then policy Value = \(\frac{100 \times 3,50,100}{97.925}\) = ₹ 3,57,518.51

Question 9.

A property worth ₹ 4,00,000 is insured with three companies. A, B, and C. The amounts insured with these companies are ₹ 1,60,000, ₹ 1,00,000 and ₹ 1,40,000 respectively. Find the amount recoverable from each company in the event of a loss to the extent of ₹ 9,000.

Solution:

Property Value = ₹ 4,00,000

Loss = ₹ 9,000

Total Value of Policies = 1,60,000 + 1,00,000 + 1,40,000 = ₹ 4,00,000

Claim = \(\frac{\text { Policy value }}{\text { Property value }}\) × Loss

Claim of company A = \(\frac{1,60,000}{40,000}\) × 9,000 = ₹ 3,600

Claim of company B = \(\frac{1,00,000}{4,00,000}\) × 9,000 = ₹ 2,250

Claim of company C = \(\frac{1,40,000}{4,00,000}\) × 9,000 = ₹ 3,150

Question 10.

A car valued at ₹ 8,00,000 is insured for ₹ 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.

Solution:

Property Value = ₹ 8,00,000

Policy Value = ₹ 5,00,000

Rate of Premium = 5% less 20%

= 5% – 20% × 5%

= (5 – 1)%

= 4%

Amount of Premium = 4% × 5,00,000 = ₹ 20,000

Loss = [100 – 60]% × Property Value

= 40% × 8,00,000

= ₹ 3,20,000

Claim = \(\frac{\text { Policy value }}{\text { Property value }}\) × Loss

= \(\frac{5,00,000}{8,00,000}\) × 3,20,000

= ₹ 2,00,000

Loss bear by owner = Loss – claim + Premium

= 3,20,000 – 2,00,000 + 20,000

= ₹ 1,40,000

Question 11.

A shop and a godown worth ₹ 1,00,000 and ₹ 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%.

Solution:

Rate of Premium = 0.80% Less 20%

= 0.80% – 20% × 0.80%

= (0.80 – 0.16)%

= 0.64%

For Shop

Property Value = ₹ 1,00,000

Policy Value = 80% × 1,00,000 = ₹ 80,000

Premium = 0.64% × 80,000 = ₹ 512

For Godown

Property Value = ₹ 2,00,000

Policy Value = 60% × 2,00,000 = ₹ 1,20,000

Premium = 0.64% × 1,20,000 = ₹ 768

∴ Total Premium = 512 + 768 = ₹ 1,280

Rate of Commission = 12%

∴ Agent Commission = 12% × 1,280 = ₹ 153.6

Question 12.

The rate of premium on a policy of ₹ 1,00,000 is ₹ 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.

Solution:

Policy Value = ₹ 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 = ₹ 55.25 per thousand p.a.

∴ Net Amount ot Premium = \(\frac{1,00,000}{1000}\) × 55.25 = ₹ 5,525

Question 13.

A warehouse valued at ₹ 40,000 contains goods worth ₹ 2,40,000. The warehouse is insured against fire for ₹ 16,000 and the goods to the extent of 90% of their value. Goods worth ₹ 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 ₹ 8,000. Find the total amount that can be claimed.

Solution:

For Warehouse

Property Value = ₹ 40,000

Policy Value = ₹ 16,000

Loss = ₹ 8,000

Claim = \(\frac{\text { Policy value }}{\text { Property value }}\) × Loss

= \(\frac{16,000}{40,000}\) × 8,000

= ₹ 3,200

For Goods

Property Value = ₹ 2,40,000

Policy Value = 90% × 2,40,000 = ₹ 2,16,000

Complete Loss = 80,000

Partial Loss = 80% × (2,16,000 – 80,000)

= 80% × 1,36,000

= ₹ 1,08,800

Claim = \(\frac{\text { Policy value }}{\text { Property value }}\) × Loss

= \(\frac{2,16,000}{24,000}\) × 1,08,800

= ₹ 97,920

∴ Total Claim = 3,200 + 97,920 = ₹ 1,01,120

Question 14.

A person takes a life policy for ₹ 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 ₹ 20 per year per thousand. Find the paid up value of the policy if he discontinuous paying premium after 10 years.

Solution:

Policy Value = ₹ 2,00,000

Rate of Bonus = ₹ 20 Per thousand p.a.

Total Bonus = \(\frac{2,00,000 \times 20}{1,000}\) = ₹ 4,000

∴ Bonus for 10 years = 4,000 × 10 = ₹ 40,000

Period of Policy = 20 years

∴ Amount of Premium = \(\frac{2,00,000}{20}\) = ₹ 10,000 p.a.

∴ Total Premium for 10 years = 10,000 × 10 = ₹ 1,00,000

∴ Paid up Value of Policy = Total premium + Total Bonus

= 1,00,000 + 40,000

= ₹ 1,40,000