Investment in Two Schemes

Video Explanation

Question

Susan invested a certain amount of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum respectively. She received Rs 1860 as annual interest. If she had interchanged the investments, she would have received Rs 20 more. Find the amount invested in each scheme.

Solution

Step 1: Let the Variables

Let the amount invested in Scheme A (8%) = ₹\(x\)

Let the amount invested in Scheme B (9%) = ₹\(y\)

Step 2: Form the First Equation

Interest from Scheme A:

\[ 0.08x \]

Interest from Scheme B:

\[ 0.09y \]

Total annual interest:

\[ 0.08x + 0.09y = 1860 \quad (1) \]

Step 3: Form the Second Equation

After interchanging the investments:

\[ 0.09x + 0.08y = 1880 \quad (2) \]

Step 4: Remove Decimals

Multiply both equations by 100:

\[ 8x + 9y = 186000 \quad (3) \]

\[ 9x + 8y = 188000 \quad (4) \]

Step 5: Solve by Elimination Method

Multiply equation (3) by 9:

\[ 72x + 81y = 1674000 \]

Multiply equation (4) by 8:

\[ 72x + 64y = 1504000 \]

Subtract:

\[ 17y = 170000 \]

\[ y = 10000 \]

Step 6: Find the Value of x

Substitute \(y = 10000\) in equation (3):

\[ 8x + 9(10000) = 186000 \]

\[ 8x + 90000 = 186000 \]

\[ 8x = 96000 \]

\[ x = 12000 \]