A invests a certain amount in a scheme at an interest rate of 5\% per annum, and B invests the remaining amount at 3\% per annum for 2 years. The total amount invested by A and B together is \$4000. If the simple interest earned by both A and B is the same, what is the amount invested by A?

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Accepted Answer

**Solution:**

1. Let the amount invested by A be $ x $. Then the amount invested by B is $ 4000 - x $.

2. Simple interest formula: $ SI = \frac{P \times R \times T}{100} $, where $P$ is principal, $R$ is rate, and $T$ is time in years.

3. Interest earned by A:
   $$
   SI_A = \frac{x \times 5 \times 2}{100} = \frac{10x}{100} = 0.1x
   $$

4. Interest earned by B:
   $$
   SI_B = \frac{(4000 - x) \times 3 \times 2}{100} = \frac{6(4000 - x)}{100} = 0.06(4000 - x)
   $$

5. Since the interests are equal:
   $$
   0.1x = 0.06(4000 - x)
   $$

6. Simplify the equation:
   $$
   0.1x = 240 - 0.06x
   $$
   $$
   0.1x + 0.06x = 240
   $$
   $$
   0.16x = 240
   $$
   $$
   x = \frac{240}{0.16} = 1500
   $$

**Answer:** \$1500

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