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?

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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: 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: Let the amount invested in Scheme Y be \( y \). Then the amount invested in Scheme X, at 18 percent, is \( 25400-y \).

Step 2: The simple interest from Scheme X over 2 years is \( \frac{(25400-y) \times 18 \times 2}{100}=0.36(25400-y) \), and from Scheme Y is \( \frac{y \times 10 \times 2}{100}=0.20y \).

Step 3: The total interest is Rs. 6,460, so \( 0.36(25400-y)+0.20y=6460 \). Expanding gives \( 9144-0.36y+0.20y=6460 \), which simplifies to \( 9144-0.16y=6460 \).

Step 4: Solving, \( 0.16y=9144-6460=2684 \), so \( y=\frac{2684}{0.16}=16775 \).
\[ \boxed{\text{Rs. } 16{,}775} \]
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Approach Solution -2

The overall two-year interest rate actually earned is \( 6460/25400 \), about 25.43 percent. We can test each option by treating it as the Scheme Y amount, computing the resulting Scheme X amount, and directly recomputing the blended two-year rate that split would produce.

  1. Rs. 8,625: Scheme X would be Rs. 16,775. The blended rate is \( \tfrac{16775 \times 36+8625 \times 20}{25400}=\tfrac{603900+172500}{25400} \approx 30.57\% \), not 25.43 percent.
  2. Rs. 16,775: Scheme X would be Rs. 8,625. The blended rate is \( \tfrac{8625 \times 36+16775 \times 20}{25400}=\tfrac{310500+335500}{25400}=25.43\% \), matching exactly.
  3. Rs. 12,240: Scheme X would be Rs. 13,160. The blended rate is \( \tfrac{13160 \times 36+12240 \times 20}{25400} \approx 28.29\% \), not 25.43 percent.
  4. Rs. 10,930: Scheme X would be Rs. 14,470. The blended rate is \( \tfrac{14470 \times 36+10930 \times 20}{25400} \approx 29.11\% \), not 25.43 percent.

Recomputing the blended two-year rate for each split shows that only Rs. 16,775 in Scheme Y reproduces the actual overall rate of 25.43 percent.

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

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