Question

Solve the following :

Stocks in a shop and godown worth ₹75,000 and ₹1,30,000 respectively were insured through an agent who receives 15% of premium as commission. If the shop was insured for 80% and godown for 60% of the value, find the amount of agent’s commission when the premium was 0.80% less 20%. If the entire stock in the shop and 20% stock in the godown is destroyed by fire, find the amount that can be claimed under the policy.

Answer 1

Given, Stock (property) value of shop = ₹75,000
Stock (property) value of godown = ₹1,30,000.
The shop was insured to 80% of its stock value.
Policy value of stock in the shop
= 80% of its property value

= ${\displaystyle \frac{80}{100}\times 75,000}$
= ₹60,000
Also, 60% of stock value of the godown was insured.
∴ Policy value of stock in the godown
= 60% of its stock value

= ${\displaystyle \frac{60}{100}\times 1,30,000}$
= ₹78,000

Total policy value = Policy value of stock in the shop + Policy value of stock in the godown
= 60,000 + 78,000
= ₹1,38,000
Rate of premium was 0.80% less 20%
i.e. 0.80 – 20% of 0.80
= 0.80 – 0.16 
= 0.64%
∴ Amount of perimum
= 0.64% of total policy value

= ${\displaystyle \frac{0.64}{100}\times 1,38,000}$
= ₹883.20
Agent’s rate of commission is 15% of total premium.

∴ Agent’s commision = 15% of total premium

= ${\displaystyle \frac{15}{100}\times 883.20}$
= ₹132.4
Now, entire stock in the shop was destroyed by fire.
∴ Loss occurred in the shop = Stock value of the shop
∴ Loss occurred on the shop = ₹75,000

∴ Claim for shop = ${\displaystyle \frac{\text{Policy value of stock in shop}}{\text{Property value of stock in shop}}\times \text{Loss in shop}}$

= ${\displaystyle \frac{60,000}{75,000}\times 75,000}$
= ₹60,000
20% of stock was destroyed by fire in the godown.
∴ Destroyed value of stock (loss) in godown
= 20% of stock value

= ${\displaystyle \frac{20}{100}\times 1,30,000}$
= ₹26,000

∴ Claim for the godown = ${\displaystyle \frac{\text{Policy value of stock in godown}}{\text{Property value of stock in godown}}\times \text{Loss in godown}}$

= ${\displaystyle \frac{78,000}{1,30,000}\times 26,000}$
= ₹15,600.
∴ Total Claim
= Claim for shop + Claim for godown
= 60,000 + 15,600
= 75,600
∴ Amount that can be claimed under the policy is ₹75,600 and commission to the agent is ₹132.40.