In what ratio must oil at rs. 62 per L mixed with oil at rs. 72 per L, so that the mixture must be worth rs. 64 per L?

Options

A. a. 1:4
B. b. 4:1
C. c. 1:3
D. d. 2:3

Answer

To solve the problem of mixing two oils priced at Rs. 62 per litre and Rs. 72 per litre to achieve a mixture worth Rs. 64 per litre, we can use the method of allegation. Here’s a step-by-step solution:

### Step 1: Identify the Prices
We have:
- Price of Oil 1 (P1) = Rs. 62 per litre
- Price of Oil 2 (P2) = Rs. 72 per litre
- Price of the mixture (Pm) = Rs. 64 per litre

### Step 2: Apply the Allegation Method
To find the ratio in which the two oils should be mixed, we will use the allegation method. We calculate the differences between the prices of the oils and the price of the mixture.

1. Calculate the difference between the price of Oil 1 and the price of the mixture:
\[ |P1 - Pm| = |62 - 64| = 2 \]

2. Calculate the difference between the price of Oil 2 and the price of the mixture:
\[ |P2 - Pm| = |72 - 64| = 8 \]

### Step 3: Set Up the Ratio
The ratio of the quantities of the two oils can be set up using the differences calculated above:
\[ \text{Ratio} = \frac{|P2 - Pm|}{|Pm - P1|} = \frac{8}{2} \]

### Step 4: Simplify the Ratio
Now simplify the ratio:
\[ \frac{8}{2} = 4 \]
Thus, the ratio of Oil 2 to Oil 1 is 4:1.

### Final Answer
The oils must be mixed in the ratio of **4:1**.

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