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.

Answer 1

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.