Multiple choice

Maya has Rs. 15,250 that she wants to divide into three parts. She wants to ensure that the simple interest earned on each part, invested for different periods and at different rates, is equal. If she invests the first part for 2 years at a rate of 4% per annum, the second part for 3 years at a rate of 6% per annum, and the third part for 4 years at a rate of 8% per annum, how much does she invest in the first part, the second part, and the third part, respectively?

  1. Rs. 7,900, Rs. 5,150 and Rs. 2,200

  2. Rs. 8,950, Rs. 4,000 and Rs. 2,300

  3. Rs. 9,000, Rs. 4,000 and Rs. 2,250

  4. Rs.10,200, Rs. 3,000 and Rs. 2,050
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since the simple interest on each of the three parts is equal, we have P1 * 2 * 4% = P2 * 3 * 6% = P3 * 4 * 8%, which simplifies to 8 * P1 = 18 * P2 = 32 * P3, or 4 * P1 = 9 * P2 = 16 * P3. This gives the ratio of the parts as P1 : P2 : P3 = 36 : 16 : 9. Dividing Rs. 15,250 in this ratio yields P1 = Rs. 9,000, P2 = Rs. 4,000, and P3 = Rs. 2,250.

AI explanation

For the simple interest on each part to be equal, the parts must be in the inverse ratio of the product of their rates and times. The products are 8, 18, and 32, so the parts are in the ratio 1/8 : 1/18 : 1/32, which simplifies to 36 : 16 : 9. Dividing the total of Rs. 15,250 in this ratio gives (36/61) * 15250 = 9000 for the first part, (16/61) * 15250 = 4000 for the second part, and (9/61) * 15250 = 2250 for the third part. She invests Rs. 9,000, Rs. 4,000, and Rs. 2,250, respectively.

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