In what proportion can water be mixed with a certain compound such that by…
2024
In what proportion can water be mixed with a certain compound such that by selling the mixture at the cost price, a profit of 60% can be made?
- A.
1:5
- B.
5:1
- C.
3:5
- D.
2:5
Attempted by 11 students.
Show answer & explanation
Correct answer: C
Solution:
Let the amount of compound be C (cost incurred) and the amount of water be W (water is free). The mixture is sold at the compound's unit cost, so selling price per unit of mixture equals cost price per unit of compound.
Total revenue when selling the mixture = (C + W) × (unit cost of compound).
Total cost = C × (unit cost of compound).
Profit = Revenue − Cost = W × (unit cost of compound).
Profit percentage = (Profit ÷ Cost) × 100 = (W ÷ C) × 100. Set this equal to 60%:
W ÷ C = 60 ÷ 100 = 0.6 ⇒ W:C = 0.6:1 = 3:5.
Check with numbers: Take compound = 5 kg (cost = 5 units) and water = 3 kg. Total sold = 8 kg at 1 unit/kg ⇒ revenue = 8; profit = 3; profit% = 3/5 × 100 = 60%.
Answer: Water and compound should be mixed in the ratio 3:5 (water : compound).