Multiple choice

Rajat lends Rs. 10,000 for 3 years at an interest rate of 15% per annum. Manoj lends the same amount for 3 years in the ratio 5 : 7 : 8 with interest rates of 8%, 15%, and x%, respectively. If Rajat earns 10% less interest than Manoj, what is the value of x?

  1. 24.125%

  2. 25.176%

  3. 23.541%

  4. 24.115%

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rajat's interest = 10000 * 3 * 0.15 = 4500. Manoj's principal is split in 5:7:8 ratio (total 20 parts). Principal 1 = 2500, P2 = 3500, P3 = 4000. Interest = 2500*3*0.08 + 3500*3*0.15 + 4000*3*(x/100) = 600 + 1575 + 120x = 2175 + 120x. Rajat earns 10% less than Manoj, so 4500 = 0.9 * (2175 + 120x). 5000 = 2175 + 120x, 2825 = 120x, x = 23.5416%.

AI explanation

Rajat earns simple interest of (10000 x 15 x 3) / 100, which equals 4500. Since Rajat earns 10% less than Manoj, Manoj earns 4500 divided by 0.9, which is 5000 in total interest. Manoj lends his principal in the ratio 5:7:8, so the interest from the three parts is (5000 x 0.08) + (7000 x 0.15) + (8000 x x / 100). This gives 400 + 1050 + 80x = 5000, and solving for x gives 80x = 3550, so x equals 23.541%.

Keep practicing — related questions