Mixtures Alligation

A trader sells 10 litres of a mixture of paints A and B, where the amount of B in the mixture does not exceed that of A. The cost of paint A per litre is Rs. 8 more than that of paint B. If the trader sells the entire mixture for Rs. 264 and makes a profit of 10%, then the highest possible cost of paint B, in Rs. per litre, is

  1. 26
  2. 16
  3. 20
  4. 22

Answer

Let the quantities of the paints A and B in the mixture sold be a litres and b litres respectively.

Value at which the entire mixture is sold = Rs. 264

Profit percent made = 10%

Value at which the entire mixture is bought = 264 × 100/110 = Rs. 240

Price at which the entire mixture is bought = Rs. 24 per litre

Let the cost of B be Rs. x per litre.

Cost of A = Rs. (x + 8) per litre

[(x + 8)a + xb]/10 = 24

Maximum cost of B will occur when a is minimum.

Since, b <= a. So, minimum value of a is 5.

Accordingly b = 5.

Then,

(x + 8)(5) + x(5) = 240

10x + 40 = 240

x = 20

The correct option is C.