Multiple choice

A man has Rs. $10,000$ to invest. He invests Rs. $4000$ at $5\%$ per annum and Rs. $3500$ at $4\%$ per annum simple interest. At what rate of interest per annum should he invest the remaining amount in order to have an yearly income of Rs. $500$

  1. $12\%$ p.a.
  2. $6.4\%$ p.a.
  3. $8\%$ p.a.
  4. $13.6\%$ p.a.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total investment is 10000. Remaining amount is 10000 - 4000 - 3500 = 2500. Interest from first part is 4000 * 0.05 = 200. Interest from second part is 3500 * 0.04 = 140. Total interest needed is 500, so interest from third part must be 500 - 200 - 140 = 160. Rate = (160 / 2500) * 100 = 6.4%.

AI explanation

The total investment is Rs. 10000, and he invests Rs. 4000 at 5 percent and Rs. 3500 at 4 percent, leaving a remaining amount of Rs. 2500. The interest from the first two investments is 5 percent of 4000 plus 4 percent of 3500, which equals 200 plus 140, giving Rs. 340. To achieve a total yearly income of Rs. 500, the remaining required interest is 500 minus 340, which is Rs. 160. Using the simple interest formula for 1 year, the needed rate is (160 times 100) divided by 2500, resulting in 6.4 percent. The required rate is 6.4 percent per annum.

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