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

Answer: 25 : 15 (or 5 : 3)

To find the correct ratio using the Rule of Alligation, we first need to determine the cost price (CP) of the mixture.

1. Calculate the Cost Price (CP) of the Mixture

• Selling Price (SP) = Rs. 98.25/kg

• Profit = 20%

• Formula: $\text{Cost Price} = \frac{\text{Selling Price}}{1 + \frac{\text{Profit\%}}{100}}$
  $\text{CP} = \frac{98.25}{1.20} = \mathbf{\text{Rs. } 81.875\text{/kg}}$

2. Apply the Rule of Alligation

Set up the cheaper oil price, dearer oil price, and the mean cost price:

• Cheaper Oil (Type 1) = Rs. 80

• Dearer Oil (Type 2) = Rs. 85

• Mean Price = Rs. 81.875

$\begin{array}{ccc} \text{Cheaper Price (80)} & & \text{Dearer Price (85)} \\ & \searrow \quad \quad \swarrow & \\ & \text{Mean Price (81.875)} & \\ & \swarrow \quad \quad \searrow & \\ (85 - 81.875) = \mathbf{3.125} & & (81.875 - 80) = \mathbf{1.875} \end{array}$

3. Simplify the Ratio

The required ratio of Type 1 to Type 2 is 3.125 : 1.875.

Multiply both sides by 1000 to remove decimals:
$3125 : 1875$

Divide both sides by 125:
$\frac{3125}{125} : \frac{1875}{125} = \mathbf{25 : 15}$

Further reducing by 5:
$\mathbf{5 : 3}$