Q.A shop worth ₹10,00,000 suffers a fire loss of ₹3,00,000. The policy carries an average clause and the claim admitted is ₹1,80,000. Find the sum for which the shop was insured (the policy value).

Rearrange the average-clause formula to solve for the sum insured.

$180000=\dfrac{S}{1000000}\times300000\Rightarrow S=\dfrac{180000\times1000000}{300000}=600000$.

Let the sum insured be $S$. The average clause gives

Solve for $S$:

Check (independent verification): with $S=₹6{,}00{,}000$ the ratio is $\dfrac{600000}{1000000}=0.6$, and $0.6\times300000=₹1{,}80{,}000$ — exactly the claim given.

Ratio method: claim ÷ loss $=\dfrac{180000}{300000}=0.6$, and this ratio equals sum insured ÷ property value, so sum insured $=0.6\times1000000=₹6{,}00{,}000$.

Multiplying instead of dividing, or putting the loss (₹3,00,000) rather than the property value in the average-clause ratio. The ratio (claim ÷ loss) equals (sum insured ÷ property value).