Multiple choice

A sum of $Rs50,000$ is lent out partly at $15\%$ p.a. and the rest at $10\%$ p.a., both at simple interest. If the total interest earned for two years is $Rs12,000,$ find the sum lent at $15\%$

  1. $Rs15,000$
  2. $Rs20,000$
  3. $Rs25,000$
  4. $Rs30,000$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let x be the sum at 15%. Then (50000-x) is at 10%. Interest = (x * 15 * 2)/100 + ((50000-x) * 10 * 2)/100 = 12000. 0.3x + 10000 - 0.2x = 12000. 0.1x = 2000. x = 20000.

AI explanation

The total interest for two years is Rs. 12,000, meaning the annual interest is Rs. 6,000, which translates to an overall annual interest rate of (6000 / 50000) * 100 = 12%. Using the method of alligation, the desired 12% rate is the weighted average of the 15% and 10% rates, yielding a ratio of amounts invested at 15% to 10% as 2 : 3. The sum invested at 15% is therefore (2 / 5) of the total Rs. 50,000, which calculates to Rs. 20,000.

Keep practicing — related questions