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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This question was previously asked in

SSC CHSL Exam 2024 Tier-I Official Paper (Held On: 04 Jul, 2024 Shift 4)

Answer 1

Given:

Principal total (P_total) = ₹8,000

Time (t) = 2 years

Interest received = ₹720

Rate of interest in scheme 1 (r₁) = 5% per annum

Rate of interest in scheme 2 (r₂) = 4% per annum

Formula used:

Simple Interest (SI) = \( \frac{P \times r \times t}{100} \)

Calculation:

Let the amount invested in scheme 1 be ₹x.

Then, the amount invested in scheme 2 = ₹(8,000 - x).

Interest from scheme 1 = \( \frac{x \times 5 \times 2}{100} \)

Interest from scheme 2 = \( \frac{(8,000 - x) \times 4 \times 2}{100} \)

Total interest = ₹720

⇒ \( \frac{x \times 5 \times 2}{100} + \frac{(8,000 - x) \times 4 \times 2}{100} = 720 \)

⇒ \( \frac{10x}{100} + \frac{64,000 - 8x}{100} = 720 \)

⇒ \( \frac{10x + 64,000 - 8x}{100} = 720 \)

⇒ \( \frac{2x + 64,000}{100} = 720 \)

⇒ 2x + 64,000 = 72,000

⇒ 2x = 72,000 - 64,000

⇒ 2x = 8,000

⇒ x = 4,000

∴ The amount of money invested in scheme 1 is ₹4,000, which is option (4).