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?
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
The correct option is (B): Rs. 16,775.
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A total of Rs. 25,400 is split between Scheme X at 18% simple interest and Scheme Y at 10% simple interest, earning Rs. 6,460 total interest over 2 years. We need the amount invested in Scheme Y. Let's check each option by working out the resulting total interest.
- Option (A): Rs. 8,625: If Rs. 8,625 is in Scheme Y, then Rs. 16,775 is in Scheme X. Interest = 16775 x 18 x 2 / 100 + 8625 x 10 x 2 / 100 = 6039 + 1725 = Rs. 7,764, more than Rs. 6,460.
- Option (B): Rs. 16,775: If Rs. 16,775 is in Scheme Y, then Rs. 8,625 is in Scheme X. Interest = 8625 x 18 x 2 / 100 + 16775 x 10 x 2 / 100 = 3105 + 3355 = Rs. 6,460, matching the given total exactly.
- Option (C): Rs. 12,240: If Rs. 12,240 is in Scheme Y, then Rs. 13,160 is in Scheme X. Interest = 13160 x 18 x 2 / 100 + 12240 x 10 x 2 / 100 = 4737.6 + 2448 = Rs. 7,185.60, more than Rs. 6,460.
- Option (D): Rs. 10,930: If Rs. 10,930 is in Scheme Y, then Rs. 14,470 is in Scheme X. Interest = 14470 x 18 x 2 / 100 + 10930 x 10 x 2 / 100 = 5209.2 + 2186 = Rs. 7,395.20, again more than Rs. 6,460.
Only Rs. 16,775 invested in Scheme Y (with the remaining Rs. 8,625 in Scheme X) produces the stated total interest of Rs. 6,460.
Therefore, the correct answer is Rs. 16,775.
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The two schemes pay simple interest at 18% and 10% per annum. Combining the interest earned across both, the overall annual rate that Rs. 25,400 effectively earned works out to \[ \frac{\text{Total interest}}{\text{Total sum}\times\text{time}}=\frac{6460}{25400\times2}=\frac{323}{2540} \] per year. To split the amounts, compare how far this blended rate sits from each scheme's own rate, since the amount in each scheme is inversely proportional to its distance from the blended rate. Using a common denominator of 12700 (since \( 100=2^2\times5^2 \) and \( 2540=2^2\times5\times127 \)): \[ \frac{18}{100}-\frac{323}{2540}=\frac{2286}{12700}-\frac{1615}{12700}=\frac{671}{12700}, \qquad \frac{323}{2540}-\frac{10}{100}=\frac{1615}{12700}-\frac{1270}{12700}=\frac{345}{12700}. \] So the amount in Scheme Y compared to the amount in Scheme X is in the ratio \( 671:345 \), since Y (the lower rate) takes the share proportional to how far X's rate is from the blend, and vice versa. With \( 671+345=1016 \) parts making up Rs. 25,400, each part is worth \( \frac{25400}{1016}=25 \), so Scheme Y gets \( 671\times25=16775 \) and Scheme X gets \( 345\times25=8625 \). Check this split against each option.
- Option (A): Rs. 8,625: This figure is exactly what the ratio split gives for Scheme X, not Scheme Y, so assigning it to Scheme Y would leave Rs. 16,775 in Scheme X instead, the reverse of what the distances from the blended rate require.
- Option (B): Rs. 16,775: This matches the amount the ratio \( 671:345 \) assigns to Scheme Y exactly, with the remaining Rs. 8,625 sitting in Scheme X, precisely as the distances from the blended rate require.
- Option (C): Rs. 12,240: This does not correspond to either side of the \( 671:345 \) split of Rs. 25,400; it neither matches the ratio's share for Y nor leaves a matching share of Rs. 13,160 for X under this proportion.
- Option (D): Rs. 10,930: This too falls outside the \( 671:345 \) division of the total sum, matching neither the required share for Scheme Y nor leaving the correct complementary share for Scheme X.
Splitting the blended rate's distance from each scheme's own rate gives the ratio \( 671:345 \), which divides Rs. 25,400 into Rs. 8,625 in Scheme X and Rs. 16,775 in Scheme Y.
Therefore, the correct answer is Rs. 16,775.
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