Problem: A depositor deposited Tk. 4,000 as x% simple interest and Tk. 5,000 at ye% simple interest. He received annual interest of Tk. 320 on his deposited amounts at “If 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.

Correct Answer: y=4

Explanation:

We know, 1 = $\frac{prt}{100}$ , WhereI= Interestp = Prinicipalt= TimeHere, according to the question for 1$^{st}$ & 2$^{nd}$ part

$\frac{400\times x\times 1}{100}+\frac{5000\times y\times 1}{100}$ = 320…………………………………..(i)

And ,$\frac{5000\times x\times 1}{100}+\frac{4000\times y\times 1}{100}$ = 310…………………………………(ii)

Now, from (i) we have,

=> $\frac{4000x}{100}+\frac{5000y}{100}$

=> $\frac{4000x\times 5000y}{100}$ = 320

=> 4,000x + 5,000y = 320 X 100

=> 1,000(4x + 5y) = 32 x 1,000

=> 4x + 5y = 32

=> 4x + 5y = 32………………. (iii)

Again, from (ii) we have,

$\frac{4000x}{100}+\frac{5000y}{100}$ = 310

=> $\frac{5000x+4000y}{100}$ = 310

=> 5,000x + 4,000y = 310 x 100

=> l,000(5x + 4y) = 31 x 1,000

=> 5x + 4y = 31 5x + 4y= 31……………………………. (iv)

Now, we have

(iii) X 4 => l6x+20y= 128

(iV) X 5=> 25x+20y= 155-9x = -27

x = $\frac{-27}{-9}$

x = 3

Now, putting x = 3 in (iii)

(4 X 3)+ 5y= 32

=> 12+5y=32

=> 5y=32-12

=> 5y=20

=> y = $\frac{20}{5}$y=4