Single correct option
In what ratio must a grocer mix rice costing ₹60 per kg with rice costing ₹80 per kg so that, after selling the mixture at ₹84 per kg, he makes a profit of 20%?
- A. 1 : 1
- B. 2 : 3
- C. 3 : 2
- D. 3 : 4
Show answer and solution
Answer: (A) 1 : 1
A selling price of ₹84/kg at 20% profit means the mixture's cost price must be 84/1.20 = ₹70 per kg.
By the rule of alligation, mix in the ratio (dearer − mean) : (mean − cheaper) = (80 − 70) : (70 − 60) = 10 : 10 = 1 : 1.
Check: equal parts of ₹60 and ₹80 rice average to ₹70/kg exactly, which at a 20% markup sells for 70 × 1.2 = ₹84 ✓.
Tip: Always convert the final selling price back to the required mean cost price before applying alligation — the ratio depends on cost prices, not selling prices.
By the rule of alligation, mix in the ratio (dearer − mean) : (mean − cheaper) = (80 − 70) : (70 − 60) = 10 : 10 = 1 : 1.
Check: equal parts of ₹60 and ₹80 rice average to ₹70/kg exactly, which at a 20% markup sells for 70 × 1.2 = ₹84 ✓.
Tip: Always convert the final selling price back to the required mean cost price before applying alligation — the ratio depends on cost prices, not selling prices.
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