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CAT 2018 [SLOT 1] Quant Question with Solution 06

Question:
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 pro?t of 10%, then the highest possible cost of paint B, in Rs. per litre, is

  1. 26
  2. 16
  3. 20
  4. 22
Show Answer
Correct Answer: 3

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=264 Profit percent made=10%

Value at which the entire mixture is bought = $264\times \frac{100}{110}=240$

Price at which the entire mixture is bought=24 per litre Let the cost of B be x per litre.

Cost of A=(x+8)per litre

$\frac{(x+8) a+x b}{10}=24$

Maximum cost of B will occur when a is minimum. b<=a. So, minimum a is 5.

Corresponding b is 5. Then (x+8)(5)+x(5)=240 x=20


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