How many kilograms of sugar costing ₹50 per kg should be mixed with 30 kg of…
2023
How many kilograms of sugar costing ₹50 per kg should be mixed with 30 kg of sugar costing ₹45 per kg so that the mixture is worth ₹48 per kg?
Answer: C. 45 kg — ConceptFor a mixture, the average cost per kilogram equals total cost divided by total mass. If x kilograms at one rate are combined with a known quantity at…
- A.
50 kg
- B.
48 kg
- C.
45 kg
- D.
42 kg
Show answer & explanation
Correct answer: C
Concept
For a mixture, the average cost per kilogram equals total cost divided by total mass.
If x kilograms at one rate are combined with a known quantity at another rate, equate the total cost of the parts to the target rate multiplied by the total mass.
Application
Let x kg be the quantity of sugar costing ₹50 per kg.
The total-cost equation is 50x + 45 × 30 = 48(x + 30).
Expanding gives 50x + 1350 = 48x + 1440, so 2x = 90.
Therefore, x = 45 kg.
Cross-check
By alligation, the ratio of ₹50 sugar to ₹45 sugar is (48 − 45):(50 − 48) = 3:2. Since 2 parts correspond to 30 kg, 3 parts correspond to 45 kg.
The required quantity is 45 kg.