CAT 2025 Slot 2 QA Question & Solution
Question
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
Options
Solution
Let coffee price = C Rs/kg and cocoa price = K Rs/kg.
From the two given mixtures:
$$0.16C + 0.84K = 240$$
$$0.36C + 0.64K = 320$$
Multiply both equations by 100 to remove decimals:
$$16C + 84K = 24000$$
$$36C + 64K = 32000$$
Subtract the first from the second:
$$(36C+64K)-(16C+84K)=32000-24000$$
$$20C - 20K = 8000 \implies C - K = 400$$
Put $$C=K+400$$ into $$16C+84K=24000$$:
$$16(K+400)+84K=24000 $$
$$16K+6400+84K=24000 $$
$$100K = 17600 \implies K = 176$$
So $$C = 176 + 400 = 576$$ (Rs/kg).
For the new mixture priced at Rs 376/kg, let the coffee fraction be p. Then
$$ p\cdot 576 + (1-p)\cdot 176 = 376$$
Upon solving $$p = \tfrac{1}{2}$$
Thus, coffee is (50%) of the new mixture. In 10 kg of this mixture, coffee = $$10\times 0.5 = 5\text{kg}$$