Mr. Lala Ram has lent some money to Aaju at `6%` p.a. and the Baaju at `8%` p:a. At the end of the year he has gain the overall interest at `7%` per annum. In what ratio has he lent the money to Aaju and Baaju? ,

Options

A. `2:3`
B. `1:1`
C. `5:6`
D. `4:3`

Answer

To solve the problem of how Mr. Lala Ram has lent money to Aaju and Baaju, we can use the method of allegations. Let's break down the steps:

### Step 1: Identify the Interest Rates
- Aaju's interest rate = 6% per annum
- Baaju's interest rate = 8% per annum
- Overall interest rate = 7% per annum

### Step 2: Set Up the Allegation
We will use the method of allegations to find the ratio in which the money is lent to Aaju and Baaju.

### Step 3: Calculate the Differences
- Difference between Baaju's rate and the overall rate:
\[ 8\% - 7\% = 1\% \]

- Difference between Aaju's rate and the overall rate:
\[ 7\% - 6\% = 1\% \]

### Step 4: Form the Ratio
Using the differences calculated:
- The ratio of the amounts lent to Aaju and Baaju is given by the inverse of the differences:
\[ \text{Ratio} = \frac{\text{Difference for Baaju}}{\text{Difference for Aaju}} = \frac{1\%}{1\%} = 1:1 \]

### Final Answer
Mr. Lala Ram has lent the money to Aaju and Baaju in the ratio of **1:1**.

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