Ankur borrowed some money from Megha at 8% p.a. simple interest and twice the amount from Harshita at 9% p.a. simple interest. He then added some more money of his own and lent the entire amount to Shalini at 10% p.a. simple interest. At the end of the year Ankur gained Rs 1,400. If Ankur lent 40,000 to Shalini, then how much did Ankur borrow from Megha.

Options

A. Rs 25,000
B. Rs 20,000
C. Rs 15,000
D. Rs 10,000

Answer

To solve the problem, we need to determine how much Ankur borrowed from Megha. Let's break down the steps systematically.

### Step 1: Define the Variables
Let the amount borrowed from Megha be \( M \). According to the problem, Ankur borrowed twice this amount from Harshita, so the amount borrowed from Harshita will be \( 2M \).

### Step 2: Calculate the Total Amount Lent to Shalini
Ankur lent a total of Rs. 40,000 to Shalini. This amount is the sum of the money borrowed from Megha, the money borrowed from Harshita, and Ankur's own money. Thus, we can express this as:
\[ M + 2M + \text{(Ankur's own money)} = 40,000 \]
This simplifies to:
\[ 3M + \text{(Ankur's own money)} = 40,000 \]

### Step 3: Calculate the Interest Earned and Paid
1. **Interest from Megha**: The interest paid to Megha at 8% for 1 year is:
\[ \text{Interest from Megha} = \frac{M \times 8}{100} = 0.08M \]

2. **Interest from Harshita**: The interest paid to Harshita at 9% for 1 year is:
\[ \text{Interest from Harshita} = \frac{2M \times 9}{100} = 0.18M \]

3. **Total Interest Paid**: The total interest paid to both Megha and Harshita is:
\[ \text{Total Interest Paid} = 0.08M + 0.18M = 0.26M \]

4. **Interest Earned from Shalini**: The interest earned from Shalini at 10% for 1 year on Rs. 40,000 is:
\[ \text{Interest Earned} = \frac{40,000 \times 10}{100} = 4,000 \]

### Step 4: Set Up the Equation for Profit
According to the problem, Ankur's profit at the end of the year is Rs. 1,400. Therefore, we can set up the equation:
\[ \text{Interest Earned} - \text{Total Interest Paid} = 1,400 \]
Substituting the values we calculated:
\[ 4,000 - 0.26M = 1,400 \]

### Step 5: Solve for \( M \)
Now, we can solve for \( M \):
1. Rearranging the equation gives:
\[ 4,000 - 1,400 = 0.26M \]
\[ 2,600 = 0.26M \]

2. Dividing both sides by 0.26:
\[ M = \frac{2,600}{0.26} \]
\[ M = 10,000 \]

### Conclusion
Ankur borrowed Rs. 10,000 from Megha.

---