Multiple choice

A company invested a total of Rs. 36 lakh in three different portfolios. A part of the amount was allocated to a high-yield bond offering 9% annual interest. The remaining amount was divided between two mutual funds in the ratio 3 : 2, earning 6% and 5% annual interest, respectively. If the total annual return from all investments was Rs. 2.56 lakh, what was the amount (in Rs. lakh) invested in the high-yield bond?

  1. 8

  2. 12

  3. 16

  4. 18
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be the amount in the 9% bond. Remaining amount = 36 - x. Mutual funds get 3/5 * (36 - x) at 6% and 2/5 * (36 - x) at 5%. Total interest = 0.09x + 0.06 * 0.6 * (36 - x) + 0.05 * 0.4 * (36 - x) = 2.56. 0.09x + 0.036(36-x) + 0.02(36-x) = 2.56. 0.09x + 0.056(36-x) = 2.56. 0.034x = 2.56 - 2.016 = 0.544. x = 16.

AI explanation

Let the amount invested in the bond be x lakh, leaving 36 minus x for the mutual funds. The two funds receive 3 parts and 2 parts, giving the equation 0.09x plus 0.06 times 0.6 of (36 minus x) plus 0.05 times 0.4 of (36 minus x) equals 2.56. Simplifying yields 0.09x plus 0.036 times (36 minus x) plus 0.02 times (36 minus x) equals 2.56. Further simplification gives 0.034x plus 2.016 equals 2.56, so 0.034x equals 0.544. Solving gives x equals 16, so the amount invested was Rs. 16 lakh.

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