Multiple choice

Two vessels A and B contain mixtures of spirit and water. A mixture of 3 parts from A and 2 parts from B is found to contain 29% of spirit and a mixture of 1 part from A and 9 parts from B is found to contain 34 per cent of spirit. Find the percentage of spirit in A and B?

  1. 35, 25

  2. 40, 20

  3. 25, 35

  4. 35,20

  5. 50, 50
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C Correct answer
Explanation

Let A = x, B = y. (3x + 2y)/5 = 29 => 3x + 2y = 145. (x + 9y)/10 = 34 => x + 9y = 340. Solving this system: x = 340 - 9y. 3(340 - 9y) + 2y = 145 => 1020 - 27y + 2y = 145 => 25y = 875 => y = 35. Then x = 340 - 315 = 25.

AI explanation

Let the percentage of spirit in vessel A be 'a' and in vessel B be 'b'. By mixing 3 parts of A and 2 parts of B, we get the equation 3a plus 2b equals 145. By mixing 1 part of A and 9 parts of B, we get the equation a plus 9b equals 340. Solving this system of linear equations by substituting a equals 340 minus 9b into the first equation yields b equals 35 and a equals 25.

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