Multiple choice

Two tins A and B contain mixtures of wheat and rice. In A, the weights of wheat and rice are in the ratio 2 : 3 and in B, they are in the ratio 3 : 7. What quantities (in kg) must be taken from A and B to form a mixture containing 5 kg of wheat and 11 kg of rice?

  1. 3 kg from A, 13 kg from B

  2. 8 kg from A, 8 kg from B

  3. 2 kg from A, 14 kg from B

  4. 6 kg from A, 10 kg from B

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be the amount from A and y be the amount from B. The wheat content is (2/5)x + (3/10)y = 5 and rice content is (3/5)x + (7/10)y = 11. Solving this system of linear equations yields x = 2 and y = 14.

AI explanation

Assume x kg is taken from tin A and y kg is taken from tin B to form the 16 kg mixture containing 5 kg of wheat and 11 kg of rice. Because the wheat to rice ratio in tin A is 2 : 3, the wheat taken from A is 2x/5; similarly, the wheat from B is 3y/10. Setting the total wheat equation 2x/5 + 3y/10 = 5 and using x + y = 16, substituting x = 16 - y gives 2(16 - y)/5 + 3y/10 = 5. Solving 64 - 4y + 3y = 50 yields y = 14, meaning x = 2. The quantities are 2 kg from A and 14 kg from B.

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