Option 3 : 15 : 32

Given :

The selling price of 180 bangles is equal to the cost price of 135 bangles

Marked price is 60% above the cost price.

Formula used :

Marked price when marked price depends on cost price

Marked price = cost price + profit% on cost price

Calculations :

According to the question

Cost price of 135 bangles = Selling price of 180 bangles

Cost price/Selling price = 4/3

Consider cost price be '4x' and selling price be '3x'

Now there is 60% on cost price to become marked price

Marked price = 4x + 60% of 4x

⇒ 4x + 2.4x

⇒ 6.4x

Now required ratio,

Selling price : Marked price = 3x : 6.4x

⇒ 30 : 64

⇒ 15 : 32

∴ The ratio of selling price to marked price is 15 : 32.