An amount of ₹8,000 was invested for 2 years, partly in scheme 1 at the rate of 5% simple interest per annum and the rest in scheme 2 at the rate of 4% simple interest per annum. The total interest received at the end was ₹720. The amount of money invested in scheme 1 is:

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`. Here is the exact formatted response: ₹4,000

The correct option is ₹4,000.

Step-by-Step Explanation:

Let the amount of money invested in Scheme 1 be $x$.

Since the total amount invested is ₹8,000, the remaining amount invested in Scheme 2 is $(8000-x)$.

The formula for Simple Interest (SI) is:

$\mathrm{SI}=\frac{P\times R\times T}{100}$

Where:

• $P$ = Principal amount
• $R$ = Rate of interest per annum
• $T$ = Time period in years (here, $T=2$ years)

1. Interest from Scheme 1 (${\mathrm{SI}}_1$):

${\mathrm{SI}}_1=\frac{x\times 5\times 2}{100}=\frac{10x}{100}$

2. Interest from Scheme 2 (${\mathrm{SI}}_2$):

${\mathrm{SI}}_2=\frac{(8000-x)\times 4\times 2}{100}=\frac{8(8000-x)}{100}=\frac{64000-8x}{100}$

3. Total Interest Received:

The total interest received at the end of 2 years is ₹720.

${\mathrm{SI}}_1+{\mathrm{SI}}_2=720$

Substitute the expressions into the total interest equation:

$\frac{10x}{100}+\frac{64000-8x}{100}=720$

Multiply both sides by 100 to clear the denominator:

$10x+64000-8x=72000$

$2x+64000=72000$

$2x=72000-64000$

$2x=8000$

$x=\frac{8000}{2}=4000$

Thus, the amount of money invested in Scheme 1 is ₹4,000.