A sugar type costing ₹14 per kg is mixed with 15 kg of another sugar type…
2019
A sugar type costing ₹14 per kg is mixed with 15 kg of another sugar type costing ₹20 per kg, such that the final mixture costs ₹18 per kg.Find the quantity of ₹14 per kg sugar.
Answer: B. 7.5 kg — Solution: Both the Alligation method and an algebraic check are given below. Given prices: cheaper sugar = ₹14/kg, dearer sugar = ₹20/kg, and mixture price =…
- A.
9.5 kg
- B.
7.5 kg
- C.
8 kg
- D.
6.5 kg
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Correct answer: B
Solution: Both the Alligation method and an algebraic check are given below.
Given prices: cheaper sugar = ₹14/kg, dearer sugar = ₹20/kg, and mixture price = ₹18/kg.
By Alligation, the differences are 20 − 18 = 2 and 18 − 14 = 4. Therefore, cheaper : dearer = 2 : 4 = 1 : 2.
If the dearer sugar is 15 kg = 2 parts, then 1 part = 15/2 = 7.5 kg. Therefore, the quantity of cheaper sugar is 7.5 kg.
Algebraic verification: Let x kg be the cheaper sugar costing ₹14/kg. The total cost is 14x + 20 × 15 = 14x + 300. The average price is 18 = (14x + 300)/(x + 15). Therefore, 18(x + 15) = 14x + 300 ⇒ 18x + 270 = 14x + 300 ⇒ 4x = 30 ⇒ x = 7.5.
Conclusion: The quantity of ₹14/kg sugar is 7.5 kg.