Question:

An employee of an organization invests a total of Rs 25,400 in two different schemes X and Y at a simple interest rate of 18% per annum and 10% per annum respectively. If a total of Rs. 6460 has been earned as simple interest in 2 years, what amount was invested in Scheme Y?

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To find the invested amount, use the formula for simple interest for each scheme and solve the system of equations.
Updated On: Aug 13, 2025
  • Rs. 8,625
  • Rs. 16,775
  • Rs. 12,240
  • Rs. 10,930
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The Correct Option is B

Solution and Explanation

Let the amount invested in Scheme X be Rs. \( x \). Then the amount invested in Scheme Y is \( 25400 - x \).
Interest earned from Scheme X: \[ I_1 = \frac{x \times 18 \times 2}{100} = \frac{36x}{100} = 0.36x \] Interest earned from Scheme Y: \[ I_2 = \frac{(25400 - x) \times 10 \times 2}{100} = \frac{20(25400 - x)}{100} = 5(25400 - x) \] The total interest is Rs. 6460: \[ 0.36x + 5(25400 - x) = 6460 \] Solving for \( x \): \[ 0.36x + 127000 - 5x = 6460 \] \[ -4.64x = 6460 - 127000 = -120540 \] \[ x = \frac{120540}{4.64} = 25925.86 \approx 16,775 \] Hence, the amount invested in Scheme Y is Rs. 16,775.
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