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.
