Given data:
- The merchant gives a discount of 16% on the face value.
- The merchant gives 1 item free on buying every 19 items.
- The merchant still has a profit of 24%.
- The face value is 30% more than the cost price of Rs. 100.

To find:
- The selling price of the items.

Solution:

Let's assume the cost price of 1 item is Rs. x.

1. Face Value:
The face value is 30% more than the cost price of Rs. 100.
So, the face value = Cost price + 30% of Cost price
= x + (30/100)x
= x + (3/10)x
= (13/10)x

2. Discount:
The merchant gives a discount of 16% on the face value.
So, the discount amount = 16% of (13/10)x
= (16/100) * (13/10)x
= (4/25)x

3. Selling Price of 1 item:
The selling price of 1 item = Face value - Discount
= (13/10)x - (4/25)x
= [(13*25) - (4*10)]/ (10*25) x
= (325 - 40)/ 250 x
= (285/250) x
= (57/50) x

4. Profit Percentage:
The merchant still has a profit of 24%.
So, the profit percentage = (Selling price - Cost price) / Cost price * 100
= [(57/50)x - x]/x * 100
= [(57x - 50x)/50x] * 100
= (7x/50x) * 100
= 14%

5. Calculation of x:
Profit percentage = 24%
(7x/50x) * 100 = 24
7x/50x = 24/100
7x/50x = 6/25
x = 6/25 * 50/7
x = 12/5

6. Selling Price:
The selling price of 1 item = (57/50) * (12/5)
= 684/250

Final Answer:
The selling price of the items is Rs. 684/250.