In what ratio should sugar costing ₹71 per kg be mixed with sugar costing ₹22 per kg so that by selling the mixture at ₹41.6 per kg, there is a profit of 30%?

Given:

Sugar A = ₹71 per kg (costlier)

Sugar B = ₹22 per kg (cheaper)

Selling Price of mixture = ₹41.6 per kg

Profit = 30%

Formula used:

Cost Price of mixture = \(\dfrac{Selling\,Price}{1 + \dfrac{Profit}{100}}\)

Mixture Ratio = Use alligation rule:
\((Costlier - Mean) : (Mean - Cheaper)\)

Calculation:

Cost Price of mixture = \(\dfrac{41.6}{1 + \dfrac{30}{100}} = \dfrac{41.6}{1.3} = 32\)

Apply alligation:

Sugar A (costlier) = ₹71

Sugar B (cheaper) = ₹22

Mean Price = ₹32

⇒ Sugar A : Sugar B = \((32 - 22) : (71 - 32)\)

⇒ Sugar A : Sugar B = \(10 : 39\)

∴ Required ratio = 10 : 39