Directions for question 8: Type in your answer in the input box provided below the question.Arjun invested ₹15,000 at 12% p.a. compound interest and ₹25,000 at 10% p.a. simple interest. Bheem invested ₹x at 8% p.a. simple interest. If, after two years, the interest received by Arjun was twice the interest received by Bheem, find x.

To solve this problem, we first need to calculate the interest received by Arjun.

1. For the compound interest part, Arjun invested ₹15,000 at 12% p.a. for 2 years. The formula for compound interest is A = P(1 + r/n)^(nt), where:

   • A is the amount of money accumulated after n years, including interest.
   • P is the principal amount (the initial amount of money).
   • r is the annual interest rate (in decimal).
   • n is the number of times that interest is compounded per year.
   • t is the time the money is invested for in years.

   Since the interest is compounded annually, n = 1. So, the formula becomes A = P(1 + r)^t.

   The interest (I) is given by A - P. So, I = P(1 + r)^t - P.

   Substituting the given values, we get I = 15000(1 + 0.12)^2 - 15000 = ₹3,384.

2. For the simple interest part, Arjun invested ₹25,000 at 10% p.a. for 2 years. The formula for simple interest is I = Prt, where:

   • I is the interest.
   • P is the principal amount (the initial amount of money).
   • r is the annual interest rate (in decimal).
   • t is the time the money is invested for in years.

   Substituting the given values, we get I = 250000.102 = ₹5,000.

So, the total interest received by Arjun is ₹3,384 + ₹5,000 = ₹8,384.

According to the problem, the interest received by Arjun was twice the interest received by Bheem. So, the interest received by Bheem is ₹8,384 / 2 = ₹4,192.

Now, we need to find the principal amount x that Bheem invested at 8% p.a. simple interest to receive ₹4,192 in 2 years. Using the simple interest formula I = Prt, we can solve for P:

P = I / (rt) = 4192 / (0.082) = ₹26,200.

So, Bheem invested ₹26,200.