Question

In what ratio should sugar costing ₹84 per kg be mixed with sugar costing ₹59 per kg so that by selling the mixture at ₹73.7 per kg, there is a profit of 10%?

• A. 6 : 18
• B. 8 : 17
• C. 7 : 19
• D. 6 : 15

Answer 1

Answer:

B. 8 : 17

The sugar costing ₹84 per kg must be mixed with the sugar costing ₹59 per kg in the ratio of 8:17.

1. Find the Cost Price (CP) of the mixture

• Selling Price (SP): ₹73.7 per kg

• Profit: 10%

• $\text{Cost Price} = \frac{\text{Selling Price}}{1 + \text{Profit Percentage}}$

• $\text{Cost Price} = \frac{73.7}{1.10} = \mathbf{67 \text{ per kg}}$

2. Apply the Alligation Method

• Dearer Sugar CP: ₹84

• Cheaper Sugar CP: ₹59

• Mean Mixture CP: ₹67

• Cheaper side calculation: $84 - 67 = \mathbf{17}$

• Dearer side calculation: $67 - 59 = \mathbf{8}$

Ratio of ₹84 sugar : Ratio of ₹59 sugar=$\mathbf{8 : 17}$