Multiple choice

Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices, per kg, of A and B are in the ratio

  1. 17 : 25

  2. 19 : 24

  3. 18 : 25

  4. 21 : 25
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let CP of A be a and B be b. SP = 40. Profit 10% means CP = 40/1.1 = 400/11. (3a+2b)/5 = 400/11 => 33a+22b = 2000. Profit 5% means CP = 40/1.05 = 4000/105 = 800/21. (2a+3b)/5 = 800/21 => 42a+63b = 4000. Solving this system gives a/b = 19/24.

AI explanation

Calculate the cost prices of the mixtures by dividing the selling price by the profit factors, yielding Rs. 400/11 per kg for the first ratio and Rs. 800/21 per kg for the second. Let the costs of tea A and B be a and b; setting up the equations 3a + 2b = 5(400/11) and 2a + 3b = 5(800/21) gives their respective values. Solving these yields a ratio of a to b equal to 19 : 24.

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