Question:medium

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?

Updated On: Jul 15, 2026
  • Rs. 8,625
  • Rs. 16,775
  • Rs. 12,240
  • Rs. 10,930
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The Correct Option is B

Approach Solution - 1

Step 1: Understanding the Question.
Rs. 25,400 is split between Scheme X at 18% simple interest and Scheme Y at 10% simple interest. Over 2 years, the total interest earned is Rs. 6,460. We need to find the amount invested in Scheme Y.

Step 2: Key Formula or Approach.
Let the amount in Scheme X be \( x \), so the amount in Scheme Y is \( 25400 - x \). Simple interest is principal times rate times time, divided by 100, so we add the two interests and set the total equal to Rs. 6,460.

Step 3: Detailed Explanation.
\[ \frac{x \times 18 \times 2}{100} + \frac{(25400 - x) \times 10 \times 2}{100} = 6460 \]
\[ 0.36x + 0.20(25400 - x) = 6460 \]
\[ 0.36x + 5080 - 0.20x = 6460 \]
\[ 0.16x = 1380 \]
\[ x = 8625 \]
So Rs. 8,625 was invested in Scheme X at 18%. The amount in Scheme Y is:
\[ 25400 - 8625 = 16775 \]

Step 4: Final Answer.
The amount invested in Scheme Y is Rs. 16,775. \[ \boxed{Rs.\ 16{,}775} \]
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Approach Solution -2

Start from a baseline where the entire Rs. 25,400 is imagined to sit in Scheme Y at 10% for 2 years. This baseline interest would be \[ 25400\times\frac{10}{100}\times2=5080. \] The actual interest earned is Rs. 6,460, which is \[ 6460-5080=1380 \] more than this baseline. Every rupee that actually sits in Scheme X instead of Y earns the higher 18% rate rather than 10%, a difference of 8% per annum, or \( 8\times2=16\% \) over the full 2 years. So the amount of money actually sitting in Scheme X is whatever amount, at this extra 16% over 2 years, produces the additional Rs. 1,380: \[ \text{Amount in X}=\frac{1380}{16\%}=\frac{1380}{0.16}=8625. \] The amount in Scheme Y is then the remainder, \( 25400-8625=16775 \). Test each option as the amount in Scheme Y under this baseline-and-shift reasoning.

  1. Option (A): Rs. 8,625: If this amount sat in Scheme Y, the remaining Rs. 16,775 would sit in Scheme X, and the extra interest above baseline would be \( 16775\times16\%=2684 \), far more than the actual excess of Rs. 1,380, so this option does not fit as the amount in Y.
  2. Option (B): Rs. 16,775: This leaves Rs. 8,625 in Scheme X, and \( 8625\times16\%=1380 \), exactly the extra interest above the all-Y baseline that is actually observed.
  3. Option (C): Rs. 12,240: This would leave Rs. 13,160 in Scheme X, giving extra interest of \( 13160\times16\%=2105.6 \), far more than the Rs. 1,380 actually earned above baseline.
  4. Option (D): Rs. 10,930: This would leave Rs. 14,470 in Scheme X, giving extra interest of \( 14470\times16\%=2315.2 \), also well above the required Rs. 1,380 excess.

Measuring how much extra interest the actual mix earns above an all-Scheme-Y baseline shows exactly Rs. 8,625 must sit in Scheme X, leaving Rs. 16,775 in Scheme Y.

Therefore, the correct answer is Rs. 16,775.

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