A depositor deposited Tk. 4,000 at x% simple interest and Tk. 5,000 at y% simple interest. He received annual interest of Tk. 320 on his deposited amounts at the year end. If he could deposit Tk. 5,000 at x% simple interest and Tk. 4,000 at y % simple interest, he would receive annual interest of Tk. 310. Find the value of x and y. (Interest)

$$\begin{gathered} we know, I=\frac{prt}{100}, where \\ I=Interest; p=Principal; T=time \\ Here, according to question for 1^{st} \& 2^{nd} part \\ \frac{4000\times x\times 1}{100}+\frac{5000\times y\times 1}{100}=320.......\left(i\right) \\ and, \frac{5000\times x\times 1}{100}+\frac{4000\times x\times 1}{100}=310.......\left(ii\right) \\ Now, from \left(i\right) we have, \\ \frac{4000x}{100}+\frac{5000y}{100}=320 \\ \Rightarrow \frac{4000x+5000y}{100}=320 \\ \Rightarrow 4000x+5000y=320\times 100 \\ \Rightarrow 4x+5y=32........\left(iii\right) \\ again, from \left(ii\right) we have, \\ \frac{5000x}{100}+\frac{4000y}{100}=310 \\ \Rightarrow \frac{5000x+4000y}{100}=310 \\ \Rightarrow 5000x+4000y=310\times 100 \\ \Rightarrow 1000(5x+4y)=31\times 1000 \\ \Rightarrow 5x+4y=31.......\left(iv\right) \\ Now, we have \\ \left(iii\right)\times 4\Rightarrow 16x+20y=128 \\ \left(iv\right)\times 5\Rightarrow 25x+20y=155 \\ \Rightarrow -9x=-27 \\ x=\frac{-27}{-9} \\ Now, putting x=3 in \left(iii\right) \\ \left(4\times 3\right)+5y=32 \\ \Rightarrow 12+5y=32 \\ \Rightarrow 5y=32-12 \\ \Rightarrow 5y=20 \\ \Rightarrow y=\frac{20}{4}=4 \end{gathered}$$

The required value, x= 3 & y = 4 .