Question

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

= ${\displaystyle \frac{80}{100}\times x}$

= ${\displaystyle \frac{4x}{5}}$

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)

= ${\displaystyle \frac{80}{100}\times (x-80,000)}$

= ${\displaystyle \frac{4(x-80,000)}{5}}$

∴ Total loss = ${\displaystyle \left[\begin{array}{c}\text{Value of completely}\\ \text{destroyed stock}\end{array}\right]+\left[\begin{array}{c}\text{Loss due to}\\ \text{reduction in value}\end{array}\right]}$

= ${\displaystyle 80,000+\frac{4(x-80,000)}{5}}$

= ${\displaystyle \frac{4,00,000+4x-3,20,000}{5}}$

= ${\displaystyle \left(\frac{80,000+4x}{5}\right)}$

Now, the merchant receives ₹ 67,200 as proportional compensation.

∴ Claim = ₹ 67,200

Since, Claim = ${\displaystyle \frac{\text{Policy value}}{\text{Property value}}\times \text{Loss}}$

∴ 67,200 = ${\displaystyle \frac{\frac{4x}{5}}{x}\times \left(\frac{80,000+4x}{5}\right)}$

∴ 67,200 = ${\displaystyle \frac{4}{5}\times \left(\frac{80,000+4x}{5}\right)}$

∴ ${\displaystyle \frac{67,200\times 5\times 5}{4}}$ = 80,000 + 4x

∴ 16,800 × 25 = 80,000 + 4x

∴  4,20,000 = 80,000 + 4x

∴ 4x = 4,20,000 – 80,000

∴ 4x = ₹ 3,40,000

∴ x = ${\displaystyle \frac{3,40,000}{4}}$ = 85,000

∴ Value of the stock is ₹ 85,000.