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A person buys tea of three different qualities at $₹ \; 800, ₹ \; 500,$ and $₹ \; 300 \; \text{per kg},$ 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 $₹ \; 700 \; \text{per kg}.$ The price, in $\text{INR per kg},$ at which she should sell the remaining tea, to make an overall profit of $50 \%,$ is

1. $675$
2. $653$
3. $692$
4. $688$

Let’s draw the table for better understanding.

$$\begin{array}{} & \text{T}_{1} & \text{T}_{2} & \text{T}_{3} \\ \text{Amount per kg:} & ₹ \;800 & ₹ \;500 & ₹ \;300 \\ \text{Quantity:} & \text{2 kg} & \text{3 kg} & \text{5 kg} \\ \text{Total amount} & ₹ \;1600 & ₹ \;1500 & ₹ \;1500 \end{array}$$
Now, we have

• Total amount $= 1600 + 1500 + 1500 = ₹ \; 4600$
• Total quantity of tea $= 2 + 3 + 5 = 10 \; \text{kg}$

She mixes all the tea and sells one-sixth of the mixture at $₹ \; 700 \; \text{per kg.}$

Selling price $= \frac{10}{6} \times 700 = \frac{7000}{6} = ₹ \; 1166.67$

In order to have an overall profit of $50 \%$ on $₹ \; 4600 = 4600 \times \frac{150}{100} = ₹ \; 6900$

Then the selling price of remaining $\left( \frac{50}{6}\right) \text{kg} = 6900 – 1166.67 = ₹ \; 5733.33$

$\therefore$ The price of tea $= \dfrac{5733.33}{\frac{50}{6}}= \frac{5733.33 \times 6}{50}= \frac{34399.98}{50} = 687.99 \cong ₹ \; 688.$

Correct Answer $: \text{D}$

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