A person invested a total sum of Rs 7900 in three different schemes of simple interest at 3%, 5% and 8% per annum. At the end of one year he got same interest in all three schemes. What is the money (in Rs) invested at 3%?

Let the sum invested in the schemes at 3%, 5% and 8% per annum be Rs. $$100x,100y,100z$$ respectively

Total sum = Rs. 7900

=> $$100x+100y+100z=7900$$

=> $$x+y+z=\frac{7900}{100}=79$$ ------------(i)

Simple interest = $$\frac{P\times r \times t}{100}$$

Interest in scheme 1 = $$\frac{100x\times3\times1}{100}=Rs.$$ $$3x$$

Similarly, interest in scheme 2 = Rs. $$5y$$ and interest in scheme 3 = Rs. $$8z$$

According to ques, => $$3x=5y=8z=k$$

=> $$x=\frac{k}{3}$$ , $$y=\frac{k}{5}$$ , $$z=\frac{k}{8}$$ -----------(ii)

Substituting it in equation (i), we get :

=> $$\frac{k}{3}+\frac{k}{5}+\frac{k}{8}=79$$

=> $$k(\frac{40+24+15}{120})=79$$

=> $$\frac{79k}{120}=79$$

=> $$k=120$$

Substituting it in equation (ii), => $$x=\frac{120}{3}=40$$

$$\therefore$$ Money (in Rs) invested at 3% = $$100\times40=Rs.$$ $$4000$$

=> Ans - (C)