Rs. 3757 is to be divided between A and B such that A’s share at the end of 7 years may be equal to B’s share at the end of 9 years. If percent be 10% per annum compound interest, B’s share is

Answer

To solve the problem of dividing Rs. 3757 between A and B such that A’s share at the end of 7 years is equal to B’s share at the end of 9 years, with a compound interest rate of 10% per annum, we can follow these steps:

### Step 1: Define Variables
Let A's share be \( X \) and B's share be \( Y \). According to the problem, we have:
\[ X + Y = 3757 \]

### Step 2: Write the Compound Interest Formula
The formula for the amount \( A \) after \( t \) years with principal \( P \) and rate \( r \) is given by:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]

### Step 3: Set Up the Equations for A and B
For A's share after 7 years:
\[ A_A = X \left(1 + \frac{10}{100}\right)^7 = X \left(1.1\right)^7 \]

For B's share after 9 years:
\[ A_B = Y \left(1 + \frac{10}{100}\right)^9 = Y \left(1.1\right)^9 \]

### Step 4: Set the Amounts Equal
According to the problem, A's share after 7 years is equal to B's share after 9 years:
\[ X \left(1.1\right)^7 = Y \left(1.1\right)^9 \]

### Step 5: Simplify the Equation
We can simplify this equation by dividing both sides by \( (1.1)^7 \):
\[ X = Y \left(1.1\right)^2 \]
\[ X = Y \cdot 1.21 \]

### Step 6: Substitute for Y
Now, substitute \( Y \) in terms of \( X \) into the first equation \( X + Y = 3757 \):
\[ 1.21Y + Y = 3757 \]
\[ 2.21Y = 3757 \]

### Step 7: Solve for Y
Now, divide both sides by 2.21 to find \( Y \):
\[ Y = \frac{3757}{2.21} \]

Calculating this gives:
\[ Y \approx 1700 \]

### Step 8: Find A's Share
Now we can find A's share using \( X = 3757 - Y \):
\[ X = 3757 - 1700 = 2057 \]

### Conclusion
Thus, B's share is:
\[ \text{B's share} = Y = 1700 \]