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

To solve the problem step by step, let's break it down:

### Step 1: Calculate the insured value of the shop.
The shop is worth Rs. 1,00,000 and is insured for 80% of its value.

\[ \text{Insured value of the shop} = 80\% \text{ of } 1,00,000 = \frac{80}{100} \times 1,00,000 = 80,000 \]

### Step 2: Calculate the insured value of the godown.
The godown is worth Rs. 2,00,000 and is insured for 60% of its value.

\[ \text{Insured value of the godown} = 60\% \text{ of } 2,00,000 = \frac{60}{100} \times 2,00,000 = 1,20,000 \]

### Step 3: Calculate the total insured value.
Now, we add the insured values of the shop and the godown to get the total insured value.

\[ \text{Total insured value} = \text{Insured value of the shop} + \text{Insured value of the godown} = 80,000 + 1,20,000 = 2,00,000 \]

### Step 4: Determine the rate of premium.
The problem states that the premium rate is 0.80% less 20%. First, we calculate 20% of 0.80%.

\[ 20\% \text{ of } 0.80\% = \frac{20}{100} \times 0.80 = 0.16\% \]

Now, we subtract this from 0.80%.

\[ \text{Rate of premium} = 0.80\% - 0.16\% = 0.64\% \]

### Step 5: Calculate the total premium.
The total premium is calculated as a percentage of the total insured value.

\[ \text{Total premium} = 0.64\% \text{ of } 2,00,000 = \frac{0.64}{100} \times 2,00,000 = 1,280 \]

### Step 6: Calculate the agent's commission.
The agent's commission is 12% of the total premium.

\[ \text{Agent's commission} = 12\% \text{ of } 1,280 = \frac{12}{100} \times 1,280 = 153.6 \]

### Final Answer:
The agent's commission is Rs. 153.6.

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