Question

In what ratio must oil worth Rs. 80/kg is mixed with oil worth Rs. 85/kg and selling the mixture at Rs.98.25/kg, there can be a profit of 20%?

• A. 4:3
• B. 5:3
• C. 5:4
• D. 3:2

Answer 1

Answer:

B. 5:3

The oil must be mixed in the ratio of 5:3.

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

The selling price (SP) is ₹98.25 with a 20% profit.
$\text{Cost Price} = \frac{\text{Selling Price}}{1 + \text{Profit Percentage}}$
$\text{Cost Price} = \frac{98.25}{1.20} = 81.875\text{ per kg}$

2. Apply the rule of alligation

Compare the cost of both oils with the mean cost price:

• Cheaper oil (Price A): ₹80

• Dearer oil (Price B): ₹85

• Mixture mean price (M): ₹81.875

3. Calculate the ratio

Subtract across to find the parts needed for each:

• Quantity of Cheaper oil = $85 - 81.875 = 3.125$

• Quantity of Dearer oil = $81.875 - 80 = 1.875$

$\text{Ratio} = \frac{3.125}{1.875} = \frac{5}{3}$

Final Answer

The required mixing ratio is 5:3.