Discussion
A wheat merchant has four varieties of wheat - A, B, C, D with him. He mixed the entire quantity of the wheat of varieties A and B together. With this mixture, if he mixes the entire quantity of wheat of variety C, which costs ₹ 20/kg, the mixture so formed would cost ₹ 25/kg. Instead, if he mixes with it the entire quantity of wheat of variety D, which costs ₹ 36/kg, the mixture so formed would cost ₹ 31 per kg. If the entire quantity of wheat of variety D is thrice that of wheat of variety C, how much would the mixture of the entire quantity of wheat of all the four varieties cost ?
Answer: A
The mixture would cost 29.5/kg (in rupees).
Let the A+B mixture weigh \(q\) kg costing \(p\) per kg, with \(c\) kg of C and \(3c\) kg of D.
\[ \begin{aligned} pq + 20c &= 25(q + c) \Rightarrow pq = 25q + 5c \\ pq + 108c &= 31(q + 3c) \Rightarrow pq = 31q - 15c \\ 6q &= 20c \Rightarrow q = \tfrac{10c}{3} \end{aligned} \]
Then \(pq = \frac{265c}{3}\), and for all four varieties:
\[ \begin{aligned} \text{cost} &= \tfrac{265c}{3} + 20c + 108c = \tfrac{649c}{3} \\ \text{weight} &= \tfrac{10c}{3} + 4c = \tfrac{22c}{3} \\ \text{rate} &= \tfrac{649}{22} = 29.5 \end{aligned} \]
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