CAT 2025 Slot 2 · Quant · Question 17

CAT 2025 Slot 2 previous year question on Averages, Mixture and Alligation, with the answer and a step-by-step solution.

Averages, Mixture and AlligationArithmeticMultiple choiceMedium
A mixture of coffee and cocoa, 16% of which is coffee, costs ₹240 per kg. Another mixture of coffee and cocoa, of which 36% is coffee, costs ₹320 per kg. If a new mixture of coffee and cocoa costs ₹376 per kg, then the quantity, in kg, of coffee in 10 kg of this new mixture is
  1. A
    4
  2. B
    6
  3. C
    2.5
  4. D
    5
Pick an option, then check.
Answer & solution

Answer: Option D

A mixture that is a fraction f coffee costs f\times \left( \text{coffee rate}\right)+\left( 1-f \right)\times \left( \text{cocoa rate}\right), which is a straight line in f.

Coffee content rises from 16% to 36%, a gain of 20 percentage points, while the price rises from 240 to 320, a gain of 80.

Scaling up, the full 100 points from pure cocoa to pure coffee cost 80\times 5=400.

Pure cocoa therefore costs 240-0.16\times 400=176 per kg, and pure coffee 176+400=576 per kg.

For the new mixture, 576f+176\left( 1-f \right)=376.

That simplifies to 176+400f=376, so 400f=200 and f=0.5.

Half of 10 kg is 5 kg of coffee.

Shortcut. Work in price differences only. From the 36% mixture at 320, the new mixture is 56 dearer. Since 80 rupees buys 20 percentage points, 56 rupees buys \frac{56}{80}\times 20=14 points. So the coffee content is 36+14=50\%, giving 5 kg — the pure rates never need to be found.

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