Average, Mixture and Alligation Question 4 - CAT 2025
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:
Step-by-Step Explanation
Let the cost price of pure coffee be C Rs./kg and pure cocoa be K Rs./kg.
- Set up the cost equations for the first two mixtures:
Mixture 1 (16% coffee, 84% cocoa) costs Rs. 240:
0.16C + 0.84K = 240 ⟹ 16C + 84K = 24000 --- (Equation 1)
Mixture 2 (36% coffee, 64% cocoa) costs Rs. 320:
0.36C + 0.64K = 320 ⟹ 36C + 64K = 32000 --- (Equation 2)
- Solve for component costs:
Subtract Equation 1 from Equation 2:
36C + 64K − 16C − 84K = 32000 − 24000
20C − 20K = 8000 ⟹ C − K = 400 ⟹ C = K + 400
Substitute C = K + 400 into Equation 1:
16(K + 400) + 84K = 24000
16K + 6400 + 84K = 24000 ⟹ 100K = 17600 ⟹ K = 176
C = 176 + 400 = 576
- Analyze the new mixture using Alligation:
The new mixture consists of pure coffee (Rs. 576/kg) and pure cocoa (Rs. 176/kg) and has a target cost of Rs. 376/kg. Apply the alligation cross-subtraction:
Ratio of Coffee to Cocoa = |376 − 176| / |576 − 376| = 200 / 200 = 1 : 1
This means coffee constitutes exactly 50% of the new mixture.
Quantity of coffee in 10 kg = 10 × 0.50 = 5 kg
Correct Option: A
💡 FundaMakers Tip:
A common trap is trying to mix the two blended mixtures together. Notice that the problem states the third formulation is a new mixture of coffee and cocoa, meaning it is built directly from the raw components. Find the individual values of C and K first, then use standard alligation to find the final blending ratio.