Subjects algebra

Gain Percent

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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%**.