Multiple choice

Three types of tea a, b and c costs Rs. 95/kg, 100/kg and 70/kg, respectively. How many kilograms of each should be blended to produce 100 kg of mixture worth Rs. 90/kg, given that the quantities of brand b and brand c are equal?

  1. 70, 15, 15

  2. 50, 25, 25

  3. 60, 20, 20

  4. 40, 30, 30

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let a, b, c be kg of teas A, B, C respectively. We have: a + b + c = 100 (total mixture), b = c (equal quantities), 95a + 100b + 70c = 90 × 100 = 9000 (total value). Substituting c = b: a + 2b = 100, and 95a + 100b + 70b = 9000. So 95a + 170b = 9000. From first equation: a = 100 - 2b. Substituting: 95(100 - 2b) + 170b = 9000. This gives 9500 - 190b + 170b = 9000, so -20b = -500, and b = 25. Then c = 25, and a = 100 - 50 = 50. Answer: 50 kg, 25 kg, 25 kg, which is option B.