A mixture of coffee and cocoa, 16% of which is coffee, costs Rs 240 per kg. Another mixture of coffee and cocoa, of which 36% is coffee, costs Rs 320 per kg. If a new mixture of coffee and cocoa costs Rs 376 per kg, then the quantity, in kg, of coffee in 10 kg of this new mixture is
Answer: D
Key idea: Find the price per kg of pure coffee and of pure cocoa from the two given mixtures.
Let coffee cost \(c\) and cocoa cost \(k\) rupees per kg.
\[0.16c + 0.84k = 240, \qquad 0.36c + 0.64k = 320.\]Subtracting: \(0.2(c - k) = 80\), so \(c - k = 400\). Substituting \(c = k + 400\) into the first equation: \(k + 64 = 240\), so \(k = 176\) and \(c = 576\).
If the new mixture is a fraction \(f\) coffee: \(176 + 400f = 376\), so \(f = \tfrac12\).
Coffee in 10 kg \(= 5\) kg.
Shortcut: Each extra 20% of coffee adds Rs 80, so every 1% adds Rs 4. Going from Rs 240 to Rs 376 adds Rs 136, i.e. 34% more coffee: \(16\% + 34\% = 50\%\).
Hence, the answer is (D) 5.