Gain Percent
1. **Problem statement:** The marked price of an electric iron is 780. The shopkeeper allows a discount of 10% and still gains 8%. We need to find the gain percent if no discount is allowed.
2. **Step 1:** Calculate the selling price (SP) when a 10% discount is allowed.
The discount is 10% of 780, so discount amount = $0.10 \times 780 = 78$.
Selling price with discount = marked price - discount = $780 - 78 = 702$.
3. **Step 2:** Using the gain percent when discount is allowed to find the cost price (CP).
Given gain percent = 8%, it means
$$\text{Gain} = 8\% \text{ of CP} = 0.08 \times CP$$
So,
$$SP = CP + \text{Gain} = CP + 0.08 \times CP = 1.08 \times CP$$
We know SP = 702, therefore
$$1.08 \times CP = 702$$
$$CP = \frac{702}{1.08} = 650$$
4. **Step 3:** Calculate the gain percent if no discount is allowed.
If no discount, SP = marked price = 780.
Gain = SP - CP = $780 - 650 = 130$.
Gain percent = $$\frac{\text{Gain}}{CP} \times 100 = \frac{130}{650} \times 100 = 20\%$$.
**Final answer:** The gain percent if no discount is allowed is **20%**.