A trader offers 25% discount on the catalogue price of radio and yet makes 20% profit. If he gains ₹ 160 per radio, what must be the catalogue price of the radio?

#### Solution

Let the catalogue (list) price of the radio be ₹ 100.

The trader offers 25% discount on the catalogue price.

∴ Trade discount = 25% of catalogue price

= 25% of ₹ 100

`= 25/100 xx 100`

∴ Trade discount = ₹ 25

Now, Selling price = Catalogue price – Trade discount

= 100 - 25 = ₹ 75

Also, he gets 20% profit.

Let the cost price be ₹ 100,

∴ Selling price = Cost price + Profit

= 100 + 20% of cost price

`= 100 + 20/100 xx 100`

= 100 + 20

= ₹ 120

∴ For selling price of ` 75,

Cost price = `(100 xx 75)/120` = ₹ 62.5

∴ Profit = Selling price – Cost price

= 75 - 62.5

∴ Profit = ₹ 12.5

Now, if the catalogue price is ` 100, then profit is ₹ 12.5.

∴ For profit of ₹ 160

Catalogue price = `(100 xx 160)/12.5` = ₹ 1280

∴ Catalogue price of the radio is ₹ 1,280.