In what ratio should sugar at 72 paise/kg be mixed with sugar at 48 paise/kg so that selling the mixture at 63 paise/kg yields a profit of 1/6 of the outlay?

Introduction / Context:
We seek a cost price (CP) for the mixture that will produce a profit of 1/6 when sold at 63 paise/kg. After finding CP_mix, apply alligation between 72p and 48p to determine the mixing ratio (in the order listed in the question).

Given Data / Assumptions:

• Prices: 72p/kg (dearer) and 48p/kg (cheaper).
• Selling price (SP) = 63p/kg.
• Profit = 1/6 of outlay ⇒ SP = CP_mix * (1 + 1/6) = CP_mix * (7/6).

Concept / Approach:
First compute CP_mix = SP / (7/6) = 63 * 6/7 = 54p. Then apply alligation: ratio (quantity at 72p) : (quantity at 48p) = (CP_mix − 48) : (72 − CP_mix).

Step-by-Step Solution:
CP_mix = 63 / (7/6) = 63 * 6/7 = 54p. Alligation differences: 72 − 54 = 18; 54 − 48 = 6. Therefore, quantities (72p : 48p) = (54 − 48) : (72 − 54) = 6 : 18 = 1 : 3.

Verification / Alternative check:
Weighted average with 1 part at 72p and 3 parts at 48p gives CP = (72 + 3*48)/4 = (72 + 144)/4 = 216/4 = 54p; selling at 63p yields profit = 9/54 = 1/6, as required.

Why Other Options Are Wrong:
3 : 1 inverts the order; 2 : 3 and 3 : 2 do not give CP 54p.

Common Pitfalls:
Using SP in alligation or reversing the ratio. Always compute CP_mix first, then use alligation with correct order.

Final Answer:
1 : 3