A vendor bought 100 Orange for rs200 he sold 20 of them at a gain of 5% at what gain percent must he sell the reminder so as to gain 30% on the whole

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Solution

Dear student
$Cost price of 100 oranges = Rs 200 ∴ Cost price of 1 orange = Rs \frac{200}{100} = Rs 2 ∴ Cost price of 20 oranges = Rs 2 \times 20 = Rss 40 Now he sold 20 of them at a profit of 5 % Profit % = \frac{Profit}{Cost price} \times 100 \Rightarrow Profit % = \frac{S . P - C . P}{C . P} \times 100 \Rightarrow 5 = \frac{S . P - 40}{40} \times 100 \Rightarrow 2 = S . P - 40 \Rightarrow S . P = 42 ∴ Selling price of 20 oranges = Rs 42 Now, to make 30 % profit on the whole, S . P of 100 oranges would be 30 = \frac{S . P - 200}{200} \times 100 \Rightarrow 60 = S . P - 200 \Rightarrow S . P = 260 So, S . P of 100 oranges = Rs 260 and S . P of initial sold 20 oranges = Rs 42 Therefore, S . P of remaining 80 should be = Rs (260 - 42) = Rs 218 Profit % = \frac{Profit}{C . P} \times 100 = \frac{S . P - C . P}{C . P} \times 100 = \frac{218 - 160}{160} \times 100 [C . P of 80 oranges = Rs 2 \times 80 = Rs 160] = 36.25 % Hence, the remaining 80 oranges should be sold at a profit of 36.25 %$
Regards

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