Question

In what ratio should sugar costing ₹78 per kg be mixed with sugar costing ₹36 per kg so that by selling the mixture at ₹86.8 per kg, there is a profit of 24%?

• A. 32 : 9
• B. 17 : 4
• C. 32 : 10
• D. 36 : 10

Answer 1

Answer:

B. 17 : 4

To find the required ratio, we first need to determine the Cost Price (CP) of the mixture using the given Selling Price (SP) and profit percentage, then apply the Rule of Alligation.

Step 1: Calculate the Cost Price of the mixture

The mixture is sold at ₹86.8 per kg with a profit of 24%.

• $\text{Selling Price (SP)} = ₹86.8$

• $\text{Profit} = 24\%$

• $\text{Cost Price (CP)} = \frac{\text{SP}}{1 + \frac{\text{Profit \%}}{100}}$

• $\text{CP} = \frac{86.8}{1.24} = \mathbf{70 \text{ per kg}}$

Step 2: Apply the Rule of Alligation

We mix two types of sugar:

1. Sugar A (Dearer): ₹78 per kg

2. Sugar B (Cheaper): ₹36 per kg

3. Mean Price (CP of Mixture): ₹70 per kg

Using the alligation diagram:

• Difference 1 (Quantity of Sugar A): $|36 - 70| = 34$

• Difference 2 (Quantity of Sugar B): $|78 - 70| = 8$

Step 3: Final Ratio

The required ratio is 34 : 8.
Simplifying by dividing both sides by 2:
$34 : 8 = 17 : 4$

The sugar should be mixed in a ratio of 17 : 4.