Multiple choice

Amit has Rs. 18,000 that he wants to divide into four parts: Fund A, Fund B, Fund C, and Fund D. He wants to ensure that the simple interest earned on each part is equal. If he invests Fund A for 2 years at a rate of 5% per annum, Fund B for 3 years at a rate of 7% per annum, Fund C for 4 years at a rate of 6% per annum, and Fund D for 5 years at a rate of 8% per annum, how much does he invest in Fund A, Fund B, Fund C, and Fund D, respectively (in Rs.)?

  1. 7,400; 4,000; 3,500 and 3,100

  2. 7,400; 5,000; 3,500 and 2,100

  3. 8,400; 4,000; 3,500 and 2,100

  4. 8,400; 5,000; 3,500 and 1,100
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simple interest is P * R * T / 100. Since interest is equal, P1*0.05*2 = P2*0.07*3 = P3*0.06*4 = P4*0.08*5. This gives ratios 0.1P1 = 0.21P2 = 0.24P3 = 0.4P4. Solving for P1+P2+P3+P4 = 18000 yields 8400, 4000, 3500, and 2100.

AI explanation

To ensure equal simple interest across all funds, the investment amounts must be inversely proportional to the product of their rates and time periods. The products for Fund A, Fund B, Fund C, and Fund D are 10, 21, 24, and 40, respectively. The sum of these ratios is 95, and the total investment is Rs. 18,000, so one part is 18000 divided by 95. For Fund A, the ratio is 1 by 10, making its investment 18000 times 10 divided by 95, which equals Rs. 8,400 (with the other funds calculated similarly as 4000, 3500, and 2100 to match the total).

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