Let the original price of the toy be ‘a’.

Given, when the list price of a toy is reduced by Rs. 2, a person can buy 2 toys more for Rs. 360.

The number of toys he can buy at the original price for Rs. 360 = 360/a

According to the question, 

⇒ 360a = (a – 2)(360 + 2a)

⇒ 360a = 360a + 2a² – 720 – 4a

⇒ a² – 2a – 360 = 0

⇒ a² – 20a + 18a – 360 = 0

⇒ a(a – 20) + 18(a – 20) = 0

⇒ (a + 18)(a – 20) = 0

⇒ a = Rs. 20