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9. Lemons are bought at the rate of 3 for ₹4. At what rate must they be sold to gain 20%?
To determine the rate at which lemons must be sold to gain a 20% profit, follow these steps:
1. Determine the cost price (C.P.) of 3 lemons: The cost price of 3 lemons is given as ₹ 4.
2. Calculate the selling price (S.P.) of 3 lemons to gain a 20% profit: To gain a 20% profit, the selling price needs to be increased by 20% over the cost price. [tex]\[
\text{Selling Price} (S.P.) = \text{Cost Price} (C.P.) \times \left(1 + \frac{20}{100}\right)
\][/tex] Plugging in the numbers: [tex]\[
\text{S.P. of 3 lemons} = ₹4 \times 1.2 = ₹4.8
\][/tex]
3. Determine the selling price (S.P.) of 1 lemon: We need to find the rate per lemon to sell them individually. Since the selling price of 3 lemons is ₹4.8, the selling price of 1 lemon is: [tex]\[
\text{S.P. of 1 lemon} = \frac{\text{S.P. of 3 lemons}}{3} = \frac{4.8}{3} = 1.6
\][/tex]
4. State the final selling price per lemon: The rate at which the lemons must be sold to gain a 20% profit is ₹1.60 per lemon (rounded to two decimal places).
Therefore, to gain a 20% profit, each lemon should be sold at ₹1.60.
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