Question

A person buys tea of three different qualities at ₹ 800, ₹ 500, and ₹ 300 per kg, respectively, and the amounts bought are in the proportion $2 : 3 : 5$. She mixes all the tea and sells one-sixth of the mixture at ₹ 700 per kg. The price, in INR per kg, at which she should sell the remaining tea, to make an overall profit of 50%, is

Accepted Answer

B. Let the amounts of tea bought be $2k, 3k, 5k$ kg. Total weight = $10k$ kg. Total Cost Price (CP) = $2k(800) + 3k(500) + 5k(300) = 1600k + 1500k + 1500k = 4600k$. Average CP per kg = $\frac{4600k}{10k} = ₹ 460$. Target Selling Price (SP) for 50% profit: Total Target SP = $1.5 	imes 4600k = 6900k$. Selling $\frac{1}{6}$ of the mixture ($=\frac{10k}{6}$ kg) at ₹ 700 per kg: $$	ext{Revenue}_1 = \frac{10k}{6} 	imes 700 = \frac{7000k}{6} = \frac{3500k}{3}$$ Remaining weight = $10k - \frac{10k}{6} = \frac{50k}{6} = \frac{25k}{3}$ kg. Let $P$ be the selling price per kg of remaining tea. $$	ext{Revenue}_2 = \frac{25k}{3} 	imes P$$ Total Revenue = $\frac{3500k}{3} + \frac{25k}{3} P = 6900k$ $$3500 + 25P = 3 	imes 6900 = 20700$$ $$25P = 17200$$ $$P = \frac{17200}{25} = 688$$.

Tea mixture pricing for profit

Explanation

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