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

2.5

✅ Correct Option: 4

Let coffee cost $c$ Rs/kg and cocoa cost $k$ Rs/kg.

From the two mixtures:

$0.16c + 0.84k = 240 \quad \cdots(1)$

$0.36c + 0.64k = 320 \quad \cdots(2)$

$(2) - (1)$ :

$0.20c - 0.20k = 80$

$c - k = 400 \quad \cdots(3)$

Substituting $c = k + 400$ in $(1)$ :

$0.16(k + 400) + 0.84k = 240$

$0.16k + 64 + 0.84k = 240$

$k = 176$ Rs/kg

$c = 176 + 400 = 576$ Rs/kg

Let the fraction of coffee in the new mixture $= f$

$576f + 176(1 - f) = 376$

$576f + 176 - 176f = 376$

$400f = 200$

$f = \dfrac{1}{2}$

Coffee in 10 kg of the new mixture $= \dfrac{1}{2} \times 10 = 5$ kg

The answer is Option 4: $5$

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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

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