A sugar costing ₹14/kg is mixed with 15 kg of a ₹20/kg sugar; the mixture…
2019
A sugar costing ₹14/kg is mixed with 15 kg of a ₹20/kg sugar; the mixture costs ₹18/kg. Find quantity of the ₹14/kg sugar.
- A.
9.5 kg
- B.
7.5 kg
- C.
8 kg
- D.
6.5 kg
Attempted by 43 students.
Show answer & explanation
Correct answer: B
Alligation method: Take differences: 20 − 18 = 2 and 18 − 14 = 4. So ratio cheaper:dearer = 2:4 = 1:2. The ₹20/kg sugar (dearer) is 15 kg = 2 parts, so 1 part = 15 ÷ 2 = 7.5 kg of the ₹14/kg sugar.
Algebraic check:
Let x be the kg of the ₹14/kg sugar.
Total cost = 14x + 20×15, total weight = x + 15, desired price per kg = ₹18.
Equation: 14x + 300 = 18(x + 15) → 14x + 300 = 18x + 270 → 30 = 4x → x = 7.5.
Conclusion: The quantity of the ₹14/kg sugar is 7.5 kg.