Kamal and Manish invested some money at 10% and 20% per annum, respectively, with interest being compounded annually. Together, they receive Rs. 1,967 as interest at the end of 2 years. If Kamal has invested 25% more than Manish, then what is the total amount (in Rs.) that both have invested?1)  57002)  60003)  63004)  7000

Let's denote the amount of money Manish invested as M. According to the problem, Kamal invested 25% more than Manish, so Kamal's investment is 1.25M.

The total interest they received after 2 years is Rs. 1967. This interest is the sum of the interests each of them received on their respective investments.

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.

In this case, interest is compounded annually (n=1), and the time of investment is 2 years (t=2). So, the formula simplifies to A = P(1 + r)^2.

We know that the total amount A is the initial investment plus the interest, so the interest I can be calculated as I = A - P. Substituting A from the formula, we get I = P(1 + r)^2 - P.

For Kamal, the interest is Ik = 1.25M(1 + 0.10)^2 - 1.25M. For Manish, the interest is Im = M(1 + 0.20)^2 - M.

The total interest is the sum of the interests each of them received, so 1967 = Ik + Im.

Solving this equation will give us the value of M, and then we can find the total investment as M + 1.25M.

Let's solve it:

1.25M(1 + 0.10)^2 - 1.25M + M(1 + 0.20)^2 - M = 1967 1.25M(1.21) - 1.25M + M(1.44) - M = 1967 1.5125M - 1.25M + 1.44M - M = 1967 0.2625M + 0.44M = 1967 0.7025M = 1967 M = 1967 / 0.7025 ≈ 2800

So, the total investment is M + 1.25M = 2800 + 1.25*2800 = 2800 + 3500 = 6300.

Therefore, the total amount that both have invested is Rs. 6300. So, the correct answer is 3) 6300.