A dealer marked his goods 20% above the cost price and allows a discount of 10%. then the gain percent is:

The correct option is 8%.

To find the overall gain percent, let us break down the problem step-by-step using a assumed Cost Price (CP).

Step 1: Assume a base Cost Price (CP)
Let the Cost Price of the goods be:
CP = 100

Step 2: Calculate the Marked Price (MP)
The dealer marks his goods 20% above the cost price.
Marked Price = CP + (20% of CP)

$\text{Marked Price}=100+\left(\frac{20}{100}\times 100\right)=100+20=120$

Step 3: Calculate the Selling Price (SP) after discount
The dealer allows a discount of 10% on the Marked Price.
Discount = 10% of Marked Price

$\text{Discount}=\frac{10}{100}\times 120=12$

Selling Price (SP) = Marked Price - Discount

$\text{Selling Price}=120-12=108$

Step 4: Calculate the Gain Percent
Gain = Selling Price - Cost Price

$\text{Gain}=108-100=8$

Since the initial Cost Price was taken as 100, the gain of 8 corresponds directly to a gain percentage:

$\text{Gain Percent}=\left(\frac{\text{Gain}}{\text{CP}}\times 100\right)\%=\left(\frac{8}{100}\times 100\right)\%=8\%$

Thus, the overall gain percent is 8%.