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Question
Solve the following :
A merchant takes fire insurance policy to cover 80 % of the value of his stock. Stock worth ₹80,000 was completely destroyed in a fire while the rest of stock was reduced to 20% of its value. If the proportional compensation under the policy was ₹67,200, find the value of the stock.
Solution
Let Property value of the stock be ₹ x.
Since, merchant insures 80% of value of the stock, ∴ Policy value = 80% of value of the stock
= `(80)/(100) xx x`
= `(4x)/(5)`
Now, stock worth ₹80,000 were completely destroyed.
∴ Remaining value of the stock
= ₹(x – 80,000)
But, this remaining stock was damaged and reduced to 20% of the book value.
∴ Loss on this stock is to the extent of 80%.
∴ Loss of the remaining stock
= 80% of ₹(x – 80,000)
= `(80)/(100) xx (x - 80,000)`
= `(4(x - 80,000))/(5)`
∴ Total loss = Value of completely destroyed stock + Loss due reduction in value
= `80,000 + (4(x - 80,000))/(5)`
= `(4,00,000 + 4x - 3,20,000)/(5)`
= `((80,000 + 4x)/5)`
Now, the merchant receives ₹67,200 as proportional compensation.
∴ Claim = ₹67,200
Since, Claim = `"Policy value"/"Property value" xx "Loss"`
∴ 67,200 = `((4x)/(5))/x xx ((80,000 + 4x)/5)`
∴ 67,200 = `(4)/(5) xx ((80,000 + 4x)/5)`
∴ `(67,200 xx 5 xx 5)/(4)` = 80,000 + 4x
∴ 16,800 x 25 = 80,000 + 4x
∴ 4,20,000 = 80,000 + 4x
∴ 4x = 4,20,000 – 80,000
∴ 4x = ₹3,40,000
∴ x = `(3,40,000)/(4)` = 85,000
∴ Value of the stock is ₹85,000.
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