**Solve the following :**

4,000 bedsheets worth ₹6,40,000 were insured for `(3/7)^"th"` of their value. Some of the bedsheets were damaged in the rainy season and were reduced to 40% of their value. If the amount recovered against damage was ₹32,000, find the number of damaged bedsheets.

#### Solution

Given, Property value of 4,000 bed sheets = ₹6,40,000

∴ Cost of 1 bedsheet = `(6,40,000)/(4,000)` = ₹160

Since, bedsheets were insured to `(3/7)^"th"` value,

Policy value = `(3/7)^"th"` of property value

= `(3)/(7) xx 6,40,000 = ₹(19,20,000)/(7)`

Let the cost of bedsheets that were damaged be ₹ x.

Since, the value of damaged bedsheets is reduced to 40% of their value.

∴ Loss on damaged bedsheets

= 60% of their value

= `(60)/(100) xx x = ₹(3x)/(5)`

Amount recovered against damage is ₹32,000

∴ Claim = ₹32,000

Claim = `"Policy value"/"Property value" xx "Loss"`

∴ 32,000 = `(((19,20,000)/7))/(6,40,000) xx (3x)/(5)`

∴ 32,000 = `(192 xx 3 xx x)/(64 xx 5 xx 7)`

∴ x = `(32,000 xx 64 xx 5 xx 7)/(192 xx 3)`

∴ x = 1,24,444.4

∴ Cost value of the damaged bedsheets is ₹1,24,444.40

∴ Number of damaged bedsheets

= `"Cost of damaged bedsheets"/"Cost of one bedsheets"`

= `(1,24,444)/(160)`

= 777.78, i.e. approx 778

∴ The number of damaged bedsheets are 778.